THE  ELEMENTS  OF 
ELECTRICITY 


BY 

WIRT  ROBINSON 

LIEUTENANT-COLONEL,    UNITED    STATES    ARMY,    PROFESSOR 

OF    CHEMISTRY,    ETC.,    UNITED    STATES 

MILITARY   ACADEMY 


SECOND    EDITION 

FIRST    THOUSAND 


NEW   YORK 

JOHN  WILEY  &  SONS,  INC. 

LONDON:    CHAPMAN    &    HALL,    LIMITED 

1914 


COPYRIGHT,  1914, 

BY 

WIRT  ROBINSON 


Stanbcpe  jprcss 

F.    H.GILSON  COMPANY 
BOSTON,  U.S.A. 


PREFACE. 


The  following  text  book  on  electricity  has  been  prepared  for 
use  of  the  Cadets  of  the  United  States  Military  Academy. 

The  course  being  required  of  all  members  of  the  third  year 
class,  explanations  have  been  given  in  more  detail  than  would  be 
necessary  were  it  elective.  Recitations  on  the  text  proper  are 
accompanied  by  the  solution  of  numerous  problems  and  class  room 
instruction  is  supplemented  by  from  eight  to  ten  lectures  and 
twenty  laboratory  periods. 

WIRT  ROBINSON. 

WEST  POINT,  NEW  YORK. 
December  18, 1913. 


iii 

285773 


TABLE  OF  CONTENTS. 


INTRODUCTORY. 

CHAPTER   1. 
Units. 

Page 

Need  of  Units — Fundamental  Units — Standard  of  Length — Metric  System 

—Units  of  Mass  and  Time— C.  G.  S.  System— Absolute  Units 1 

CHAPTER  2. 
Electricity. 

Origin  of  Name — Divisions  of  Subject 6 


PART  I. 
STATIC  ELECTRICITY. 

CHAPTER  3. 
Electric  Attraction  and  Repulsion. 

Electric  Attraction — Electric  Charge — Conductors  and  Non-Conductors — 
All  Bodies  Susceptible  of  Electrification — Electric  Repulsion — Two 
Kinds  of  Electrification — Simultaneous  Production  of  Equal  Amounts 
— Electroscopes — Theories  of  Electricity 9 

CHAPTER  4. 
Electrostatic  Induction. 

Electrification  by  Influence — Distribution  of  Induced  Charge — Attraction 
and  Repulsion  Explained — Amount  of  Induced  Charge — Separation 
of  Induced  Charges— Free  and  Bound  Charges— Gold  Leaf  Electro- 
scope— Electrophorus 17 

CHAPTER   5. 
Distribution  of  Charge. 

Charge  on  Non-Conductor — On  Conductor — Confined  to  Surface— Biot's 
Experiment — Distribution  of  Charge — Surface  Density — Effect  of 
Points— Franklin's  Experiment— Other  Experiments— Division  of 
Charge 24 


vi  TABLE  OF  CONTENTS. 

Page 

CHAPTER   6. 
Electrical  Machines. 

Kinds — Frictional  Machines — Cylinder  Machine — Toepler's  Machine — 
Holtz's  Machine — Electrical  Diagrams 30 

CHAPTER   7. 
Laws  of  Electric  Attraction  "and  Repulsion. 

Coulomb's  Torsion  Balance — Law  of  Inverse  Squares — Variation  of  Force 
with  Charges — with  Intervening  Medium — Unit  Quantity  of  Elec- 
tricity    37 

CHAPTER   8. 
Electric  Field. 

Electric  IJield — Intensity — Direction — Lines  of  Force — Graphic  Represen- 
tation of  Field— Tubes  of  Force — Lines  from  Unit  Charge — Gauss' 
Theorem — Field  about  Uniformly-Charged  Sphere — near  Uniformly- 
Charged  Plane — Force  Exerted  upon  Internal  Point  by  Uniformly- 
Charged  Sphere — Charge  Resides  on  Surface 43 

CHAPTER   9. 
Potential. 

Cause  of  Movement  of  Electric  Charges — Physical  Analogues  of  Electric 
Potential — Mechanical  Potential — Electric  Potential — Zero  Potential 
— Potential  at  Point  Due  to  a  Charge — Expression  for  Electric  Force 
— Electromotive  Force — Practical  Unit  of  E.  M.  F. — Summary 51 

CHAPTER   10. 
Electrostatic  Capacity. 

Electrostatic  Capacity — Capacity  of  Sphere — Case  of  Two  United  Spheres 
— of  Two  Coalescing  Spheres — Condensers — Invention  of  Leyden  Jar 
— Explanation  of  Leyden  Jar — Location  of  Charge  of  Condenser — 
Capacity  of  Spherical  Condenser — of  Plate  Condenser — Dielectric 
Capacity — Determination — Dielectric  Capacity  of  Various  Sub- 
stances— Dielectric  Strength — Commercial  Condensers — Practical 
Unit  of  Capacity — Work  Expended  in  Charging  a  Condenser — Energy 
of  a  Condenser 59 

CHAPTER   11. 
Electrostatic  Measurements. 

Electrostatic  Measurements — Unit  Jars — Principle  of  Electrometers — 
Attracted  Disc  Electrometer — Quadrant  Electrometer 77 


TABLE  OF  CONTENTS.  vii 

Page 
PART  II. 

MAGNETISM. 

CHAPTER   12. 
Magnets. 

Natural  Magnets — Lodestones — Fables  of  Ancients — Doctor  Gilbert — 
Artificial  Magnets — Magnetic  Poles — Poles  Inseparable — Magnetic 
Attraction — Mutual  Action  of  Magnets — Why  Needle  Points  North 
and  South — Poles  Misnamed — Magnetization  by  Induction — Induc- 
tion— Induction  Takes  Place  through  Space — Magnetic  Attraction 
Explained — Other  Magnetic  Substances — Diamagnetism 85 

CHAPTER   13. 
Measurement  of  Magnetic  Forces. 

Coulomb's  First  Law — Lifting  Power  of  Magnets — Strength  of  Magnets — 
Magnetic  Pole  Defined — Measurement  of  Magnetic  Forces — Cou- 
lomb's Second  Law — Method  by  Oscillations — Magnetic  Moment — 
Experimental  Proof  of  Law  of  Inverse  Squares — Unit  Magnetic  Pole .  93 

CHAPTER   14. 
The  Magnetic  Field. 

Magnetic  Field — Direction — Intensity — Magnetic  Lines  of  Force— Map- 
ping Lines  of  Force — Permanent  Record  of  Magnetic  Figures — Com- 
pounding Magnetic  Fields — Properties  of  Magnetic  Lines  of  Force — 
Magnetic  Lines  Pass  Preferably  through  Magnetic  Substances — Law 
of  Maximum  Flux — Graphic  Representation  of  Intensity  of  Magnetic 
Field — Comparison  of  Magnetic  Fields — Tangent  Law — Sine  Law — 
Determination  of  Strength  of  Magnetic  Field — Turning  Moment  of 
Magnets 101 

CHAPTER   15. 
Theory  of  Magnetism. 

Magnetism — Molecular  Magnetism — Ewing's  Theory — Magnetization  Ac- 
companied by  Molecular  Movement — Effect  of  Vibration— Effect  of 
vHeat— Effect  of  Solution 118 

CHAPTER   16. 
Manufacture  of  Magnets. 

Most  Suitable  Metal — Principle  of  Manufacture — Method  by  Single 
Touch — Divided  Touch — Magnetization  by  Electric  Current — Con- 
sequent Poles — Magnetization  Confined  to  Outer  Layers — Aging  of 
Magnets 123. 


Vlll  TABLE  OF  CONTENTS. 

Page 

CHAPTER   17. 
Terrestrial  Magnetism. 

Location  of  Earth's  Magnetic  Poles — Magnetic  Declination — Isogonic 
Chart — Magnetic  Dip — Dipping  Needle — Isoclinic  Chart — Magnetic 
Intensity — Magnetic  Elements — Variations — Secular  Change  in  Dec- 
lination and  Dip — Diurnal  Change  in  Declination — Annual  Change 
in  Declination — Magnetic  Storms — Theories  of  Earth's  Magnetism — 
Mariner's  Compass — Adjustments 127 

PART  HI. 
VOLTAIC  ELECTRICITY. 

CHAPTER   18. 
Discoveries  of  Gaivani  and  Yolta. 

Galvani's  Discovery — Volta's  Investigations — Volta's  Contact  Series — 
Contact  Theory — Later  Theory — Voltaic  Pile — Circlet  of  Cups — 
Source  of  Electrical  Energy 145 

CHAPTER   19. 
The  Simple  Cell. 

Simple  Voltaic  Cell — Material  Used  for  Elements — Chemical  Action — 
Local  Action — Remedy — Polarization — Depolarizers — Requirements 
of  a  Voltaic  Cell 154 

CHAPTER  20. 
Kinds  of  Cells. 

Great  Variety  of  Cells — Classification — Grove — Bunsen — Bichromate — 
Daniell — Gravity — Edison-Lalande — Leclanche — Dry  Cells — Need  of 
Standard  Cells — Clark's  Cell — Weston's  Standard  Cell — Conven- 
tional Sign  for  Cell 160 

CHAPTER  21. 
The  Electric  Current  and  Its  Chemical  Action. 

Electric  Current — No  Current  unless  Circuit  Complete — Direction  of 
Flow — Decomposition  of  Water — Electrolysis  of  Water — Faraday's 
Terminology — Substances  Subject  to  Electrolysis — Electrolysis  of 
Fused  Compound — of  a  Base — of  a  Metallic  Salt — Electro-Chemical 
Classification  of  Elements — Faraday's  First  Law — Voltameter — The 
Coulomb  and  Ampere — Equality  of  Current  at  Every  Cross-Section — 
Corollary — Faraday's  Second  Law — Electro-Chemical  Equivalent — 
Definition  of  Ampere  in  Terms  of  Silver — Applications  of  Electrolysis 
— Refining  of  Copper — Electroplating — Electrotyping 170 


TABLE  OF  CONTENTS.  ix 

Page 

CHAPTER   22. 
The  Storage  Battery. 

Reversibility  of  Cells — Storage  Battery — Elements  of  a  Secondary  Cell — 
Preparation  of  Plates — Plante  Cell — Chloride  Accumulator — Shape 
and  Size  of  Plates — Grouping  of  Plates — Reactions — Charging — 
Indications  of  Charge — Troubles  of  Lead  Batteries — Care — Objections 
— Edison  Storage  Battery — Reactions — Charging — Advantages  and 
Disadvantages — Use  of  Storage  Batteries 182 

CHAPTER  23. 
Theory  of  Electrolytic  Dissociation. 

Interdependence  of  Physical  Sciences — Laws  of  Variation  of  Gaseous 
Pressure — Decomposition  and  Dissociation — Example  of  Dissociation 
by  Heat — Osmosis  and  Osmotic  Pressure — Demonstration — Measure- 
ment of  Osmotic  Pressure — Observations  of  Pfeffer — Osmotic  Pressure 
Follows  Laws  of  Gaseous  Pressure — Van't  Hoff's  Generalization — 
Exceptions — Dissociation  Theory  of  Arrhenius — Why  lonization 
Takes  Place  in  Solutions — How  lonization  Takes  Place — lonization 
Incomplete — Demonstration  of  Free  Ions — Ions  not  from  Same  Mole- 
cule— Grotthus'  Theory — Electrolytes  and  Non-Electrolytes — Elec- 
trolytic Properties  Depend  upon  lonization — Vapor  Tension — Solution 
Tension — Theory  Applied  to  Simple  Cell — Atomic  Character  of  Elec- 
tricity— Scope  of  Theory 198 

CHAPTER  24. 
Resistance. 

Resistance — Example  of  Effect — Practical  Unit — The  Ohm — Laws  of 
Resistance — Variation  with  Length — with  Cross-Section — Specific 
Resistance — Variation  with  Temperature — Platinum  Thermometer — 
Ohm  Denned  in  Terms  of  Column  of  Mercury — Resistance  and  Con- 
ductance— Resistance  of  Conductors  in  Parallel — Internal  Resistance 
of  Cells— Wire  Tables— Circular  Measure  of  Wires. .  .  213 


CHAPTER  25. 
Ohm's  Law. 

Ohm's  Law — Drop  of  Potential — Law  Applies  to  Any  Portion  of  Circuit — 
Division  of  Current  in  Divided  Circuit — Shunts — Rheostats — Kir- 
choff's  Laws — Lost  and  Useful  Volts — Short  Circuit — Definitions 
Based  on  Ohm's  Law. .  .  223 


X  TABLE  OF  CONTENTS. 

CHAPTER  26. 
Measurement  of  Resistance. 

Measurement  of  Resistance — Drop  of  Potential  Proportional  to  Resistance 
— Measurement  by  Drop  of  Potential — Resistance  Coils — Drop  in 
Divided  Circuit — Principle  of  Wheatstone  Bridge — Arrangement  of 
Resistances — Evolution  in  Form — Operation  of  Measurement — 
Bracketing — Order  of  Closing  Keys — Ratio  to  Use — Bridge  with  Re- 
versible Ratios — Dial  Bridge — Resistances  that  may  be  Measured — 
Slide  Wire  Bridge — Measurement  of  High  Resistance — Resistance  of 
Electrolytes — Internal  Resistance  of  Cells 233 

CHAPTER   27. 
The  Potentiometer. 

Measurement  of  E.  M.  F.  of  Cells — Preliminary  Arrangement  of  Poten- 
tiometer— Calibration — Measurement 248 

CHAPTER  28. 
Grouping  of  Cells  in  Batteries. 

Grouping  of  Cells — in  Series — in  Parallel — Comparison  of  Two  Groupings 
— Analogy  between  Cells  and  Pumps — Multiple  Grouping — Maximum 
Current — Diagrams — Cost  of  Power  from  Primary  Cells < 251 


PART  IV. 
ELECTRO-MAGNETICS. 

CHAPTER  29. 
Magnetic  Field  About  a  Wire  Carrying  a  Current. 

Oerstedt's  Discovery — Right  Hand  Rule  for  Deflection  of  Needle — Mag- 
netic Field  about  Wire — Direction — Clock  Rule — Wire  Carrying  a 
Current  is  not  a  Magnet — Rotation  of  Magnetic  Pole  by  Current — of 
Current  by  Pole — Left  Hand  Rule  for  Direction  of  Motion — Intensity 
of  Field  about  Straight  Conductor — Field  on  Axis  of  Circular  Coil — 
Absolute  Unit  of  Current — Force  Exerted  by  Magnetic  Field  upon 
Conductor  Carrying  a  Current — Work  Done  in  Moving  across  a  Field 
a  Conductor  Carrying  a  Current — Energy  Expended  on  an  Electro- 
Magnetic  Field — Force  between  Parallel  Conductors  Carrying  Cur- 
rents    259 

CHAPTER  30. 
Galvanoscopes  and  Galvanometers. 

Galvanoscopes — Increase  of  Sensitiveness — Schweigger's  Multiplier — 
Methods  of  Weakening  Controlling  Force — Haiiy's  Method — Astatic 
Combinations — Magnetic  Shells — De  La  Rive's  Battery — Maxwell's 


TABLE  OF  CONTENTS.  xi 

Page 

Law  —  Galvanometers  —  Tangent  Galvanometer  —  Measurement  of 
Current  by  Tangent  Galvanometer — Sine  Galvanometer — Mirror 
Galvanometer — Suspended  Coil  Galvanometer — Damping — Galvan- 
ometer Shunts — Universal  Shunt — Weber's  Electro-Dynamometer — 
Siemen's  Electro-Dynamometer — Ballistic  Galvanometer 274 

CHAPTER   31. 
Electric  Magnetization  of  Iron  and  Steel. 

Solenoid — Equivalent  to  Bar  Magnet — Intensity  of  Field  on  Axis — Am- 
pere Turns — Variation  of  Field  with  Current — Effect  of  Material  of 
Core  on  Field — Permeability — Magnetic  Saturation — Curves  of  Mag- 
netization— Ewing's  Theory  of  Molecular  Magnetism — Hysteresis — 
Cycle  of  Magnetization — Energy  Loss  due  to  Hysteresis — Law  of 
Magnetic  Circuit — Calculation  of  Flux — Diamagnetism 295 

CHAPTER   32. 
Electro-Magnets. 

Electro-Magnets — Rules  for  Polarity — Value  of  Electro-Magnets — Trac- 
tive Power — Shape — Use — Lifting  Weights — Electric  Bells — Tele- 
graph— Morse  Telegraph — American  System — Overload  Switch — 
Underload  Switch 310 

CHAPTER   33. 
Induction. 

Faraday's  Discovery  of  Induction — Faraday's  Second  Discovery — Inertia 
of  Electro-Magnetic  Fields — Explanation  Applied  to  Magnet  and  " 
Coil — to  Two  Coils — Rule  for  Direction  of  Induced  E.  M.  F. — Right 
Hand  Rule — Mechanical  Production  of  Electric  Current — Cutting  of 
Lines  of  Force — Relation  between  Rate  of  Cutting  and  Resulting  E. 
M.  F. — Absolute  Electro-Magnetic  Unit  of  E.  M.  F. — Practical  Unit 
of  E.  M.  F.,  the  Volt — Eddy  Currents — Foucault's  Experiments — 
Lenz's  Law — Transformers — Self-Induction — Measure — Inductance 
— Expression  for  Inductance  of  Coil — Helmholtz's  Equation — Induced 
E.  M.  F.  at  Make  and  Break — Induction  Coil — Use  of  Condenser — 
Bell  Telephone — Transmitter — Operation  of  Telephone 321 

CHAPTER   34. 
Ammeters  and  Voltmeters. 

Electrical  Quantities  to  be  Measured — Effects  Used  in  Measurements — 
Effect  Best  Adapted  for  Measurement — Electro-Chemical  Effect  Se- 
lected— Why  Silver  Selected — Reason  for  Weight — Electro-Chemical 
Effect  Unsuitable  for  Industrial  Needs — Electro-Magnetic  Effect 


Xll  TABLE  OF  CONTENTS. 

Page 

best  for  Practical  Measurements — Calibration  of  Galvanometer — 
Difference  between  Ammeters  and  Voltmeters — Ammeters — Voltmeter 
between  Two  Points  of  a  Circuit — E.  M.  F.  of  a  Cell  or  Battery — 
Classification  of  Ammeters  and  Voltmeters — Hot  Wire  Instruments — 
Moving  Iron  Instruments — Switchboard  Shunts — Weston  D.  C.  Am- 
meter— Weston  D.  C.  Voltmeter — Multipliers — Weston  D.  C.  A.  C. 
Voltmeter — Thomson  Inclined  Coil  Instruments — Use  of  Transform- 
ers with  A.  C.  Instruments — Milli voltmeters — Millivoltmeters  as 
Ammeters  — Millivoltmeter  Shunt 349 

CHAPTER  35. 
Heating  Effect  of  Electric  Current. 

Work  done  by  Electric  Current — Determination  of  Laws  of  Heating  Effect 
— The  Joule — Theoretical  Deduction  of  Joule's  Law — Electric  Heating 
of  Wires — Calculation  of  Temperature — Localizing  the  Heating  Effect 
— Electric  Fuzes — Electric  Welding — Electric  Arc — Electric  Furnace 
— Moissan's  Furnace — Manufacture  of  Carborundum — Manufacture 
of  Aluminum — Electric  Iron  Furnaces — The  Induction  Furnace 376 

CHAPTER   36. 
Electric  Power. 

Power  Defined — Horse  Power — Expression  for  Electric  Power — Develop- 
ment of  Power  in  a  Battery — Units  of  Electric  Power — Measurement 
of  Power  by  Electro-Dynamometer — Indicating  Wattmeter — Integrat- 
ing Wattmeter — Electrical  Transmission  of  Power — Considerations 
Affecting  Electrical  Transmission  of  Power 387 

CHAPTER  37. 
Electric  Lighting. 

The  Electric  Light — Incandescent  Lamp — Carbon  Filament — Manufacture 
of  the  Lamp — Recent  Incandescent  Lamps — Nernst  Lamp — Candle 
Power — Photometry — Life  of  Incandescent  Lamp — Efficiency — Con- 
trol of  Light — Grouping  of  Incandescent  Lamps — Arc  Light — Car- 
bons— Requirements  of  Arc  Light  Mechanism — Clutch — Constant 
Potential  Arc  Lamp — Constant  Current  Arc  Lamp — Enclosed  Arc — 
Flaming  Arc — Magnetite  Arc  Lamp — Efficiency  of  Arc  Lights — 
Luminous  Vapor  Lamps — The  Moore  Light — Cooper-Hewitt  Mercury 
Vapor  Lamp 397 

CHAPTER  38. 
T  her  mo-Electrics. 

Seebeck's  Discoveries — Thermo-Electric  Inversion — The  Peltier  Effect- 
Thomson  Effect — Thermopile — Radiometer — Radio-Micrometer.  .  .416 


TABLE  OF  CONTENTS.  xiii 

Page 
CHAPTER   39. 

Remarks  on  Certain  Electric  Units. 

Two  Systems  of  Electric  Units — Units  of  Current  and  Quantity — Units  of 
Electro-Motive  Force — Primary  Electro-Magnetic  Units — Dimen- 
sional Formulae — Dimensional  Formula  of  Electro-Magnetic  Resist- 
ance— Resistance  Expressed  as  Velocity — Absolute  Measurement  of 
Resistance — The  Ohm — The  Ampere — The  Volt — Resume — Compari- 
son of  the  dimensional  Formulae  in  the  Two  Systems — Explanation 
of  Lack  of  Agreement 423 

PART  V. 
ELECTRO-MECHANICS. 

CHAPTER  40. 
Direct  Current  Generators. 

Electro-Mechanics — Classes  of  Electrical  Machines — Coil  Rotating  in  a 
Magnetic  Field — Calculation  of  E.  M.  F.  of  Rotating  Coil — Produc- 
tion of  Current  by  Rotating  Coil — Alternating  Current — Graphic 
Representation  of  Alternating  E.  M.  F.  and  Current — Rectification  of 
Alternating  Current — Increase  in  Number  of  Turns  of  Coil — Increase 
in  number  of  Coils — Open  and  Closed  Coils — Essential  parts  of  D.  C. 
Generator — The  Field — Excitation  of  Field  Magnets — Methods  of 
Self-Excitation — Control  of  Field — Armature  Core — Classes  of  Arma- 
tures— The  Commutator — Brushes — Ring- Wound  Generator — Arma- 
ture Reaction — Commutation — Sparking — Multipolar  Generators — 
Advantages  of  Multipolar  Generators — Drum  Windings — Plane  De- 
velopment of  Drum- Winding — Star  Development  of  Drum- Winding — 
Calculation  of  E.  M.  F.  of  Generator — Switchboards — Example  of 
Switchboard — Coupling  of  Generators;  Three- Wire  System 433 

CHAPTER  41. 
Generator  Characteristics. 

Adaptation  of  Generator  to  Work  Required — Characteristics — Magneti- 
zation Characteristic — Characteristic  of  Series  Generator — Critical 
Resistance — Characteristic  of  Shunt  Generator — Compound  Gener- 
ator— Over-Compounding 466 

CHAPTER   42. 
Direct  Current  Motors. 

The  Motor  and  the  Generator  Identical — Explanation  of  Motion — Power 
Developed  by  a  Motor — Counter  Electro-Motive  Force — Relation  Be- 
tween Counter  E.  M.  F.  and  Power  Developed — Reading  of  Voltmeter 
Across  Seat  of  Counter  E.  M.  F. — Efficiency  of  Motors — Maximum 


Xiv  TABLE  OF  CONTENTS. 

Page 

Output  of  Power — Classes  of  D.  C.  Motors — The  Shunt  Motor — 
Control  of  Speed  of  Shunt  Motors — Starting  Box  for  Shunt  Motors — 
Series  Motors — Speed  of  Series  Motors — Change  of  Direction  of 
Rotation — Motor-Generators 474 


CHAPTER  43. 
Alternating  Currents. 

Alternating  E.  M.  F.  and  Current — Why  Considered  Separately — Cycle, 
Period  and  Frequency — Phase — Vector  Diagrams — Composition  of 
Alternating  E.  M.  F.s — Value  of  an  Alternating  Current — Self  Induc- 
tion— Inductance — Inductance  and  Resistance — Alternating  E.  M.  F. 
in  a  Circuit  having  Resistance  and  Inductance — Graphic  Construction 
of  E.  M.  F.  and  Current  Curves — Inductive  Reactance — Impedance — 
Choke  Coils — Explanation  of  Operation  of  Choke  Coils — Inductance 
and  Resistance  in  Series — Inductance  and  Resistance  in  Parallel — 
Capacity — Condenser  in  an  Alternating  Current  Circuit — E.  M.  F. 
and  Current  Curves  in  Case  of  Capacity — Capacity  Reactance — 
Alternating  E.  M.  F.  in  Circuit  containing  Resistance,  Inductance 
and  Capacity — Electric  Resonance — Resonance  with  Inductance  and 
Capacity  in  Series — Resonance  with  Inductance  and  Capacity  in 
Parallel — Power  in  an  Alternating  Current  Circuit — Power  Factor . .  488 


CHAPTER  44. 
Alternating  Current  Generators. 

Alternators — Field  Excitation  of  Alternators — Compound  Alternators — 
Alternators  Usually  Multipolar — Classes  of  Alternators — Alternators 
with  Revolving  Armatures — Alternators  with  Revolving  Field — The 
Inductor  Alternator — Polyphase  Alternators — Tri-Phase  Alternators 
—  Tri-Phase  Delta-Connection  —  Tri-Phase  Y-connection  —  Trans- 
formation of  Direct  and  of  Alternating  Currents — Transformers — 
Operation  of  Transformer— Connection  of  Transformers — Auto-Trans- 
formers— Rectification  of  Alternating  Current — The  Mercury  Arc 
Rectifier — Rectification  of  Single-Phase  Current — Comparison  of 
Alternating  and  Direct  Currents .  515 


CHAPTER  45. 
Alternating  Current  Motors. 

Alternating  Current  Motors — Classes  of  A.  C.  Motors — Series  Motors — 
Synchronous  Motors — Operation  of  Synchronous  Motors — The  Re- 
pulsion Motor — Principle  of  Induction  Motor — Production  of  Rotat- 
ing Field — The  Induction  Motor .533 


TABLE  OF  CONTENTS.  XV 

Page 

PART  VI. 
HIGH  POTENTIAL. 

CHAPTER  46. 
Discharge  of  Electricity  Through  Gases. 

High  Potential — Conductivity  of  Gases — Discharge  Through  Moderate 
Vacua — Effect  of  Magnetic  Field  on  Positive  Column — Discharge 
Through  High  Vacua — Cathode  Rays — Nature  of  Cathode  Rays — 
Effect  of  Magnetic  Field  on  Cathode  Rays— Effect  of  Electric  Field 
upon  Cathode  Rays — Nature  of  Charge  Carried  by  Corpuscles — 
Positive  Rays — Lenard  Rays — X-Rays — Becquerel  Rays — Increase 
of  Conductivity  of  Gases — lonization  of  Gases — Investigation  of 
Corpuscles — Velocity  of  Corpuscles — Mass  of  Corpuscle — Nature  of 
Corpuscles 543 

CHAPTER  47. 
Electric  Oscillations. 

Henry's  Theory  of  Oscillatory  Discharge  of  Leyden  Jar — Thomson's  Math- 
ematical Proof  of  Oscillation — Feddersen's  Experiment  with  Revolving 
Mirror — Explanation  of  Oscillation — Maxwell's  Electro-Magnetic 
Theory — Electric  Elasticity — Electric  Density — Velocity  of  Propaga- 
tion of  Electric  Wave — Hertz's  Confirmation  of  Maxwell's  Theory — 
Further  Experiments  by  Hertz — Length  of  Electro-Magnetic  Waves — 
Tuning  of  the  Resonator — Principle  of  Wireless  Telegraphy — The 
Aerial — The  Transmitter — Coupled  Circuits — Tuning  of  Coupled  Cir- 
cuits— Branley's  Coherer — Operation  of  Receiving  Circuit — Use  of 
Telephone  and  Detectors — Tuning  of  Receiving  Circuits — Distance 
Attained  by  Wireless  Telegraphy 556 


INTRODUCTORY. 


CHAPTER  1. 

UNITS. 

1.  Need  of  Units. — In    the    orderly   study   of    any   concrete 
science  we  early  encounter  the  necessity  for  dealing  with  quanti- 
ties.   Quantities  may  be  specified  and  an  accurate  conception  of 
them  conveyed  to  others  only  by  stating  how  many  times  greater 
or  less  they  are  than  some  like  quantity  of  which  there  is  common 
knowledge.    Those  quantities  employed  as  bases  of  comparison 
are  called  units. 

2.  Electrical  Units  to  be  Defined  Later. — In  beginning  a  study 
it  might  seem  logical  that  we  should  first  define  the  units  to  be 
used,  but  in  electricity  the  number  of  units  is  perhaps  greater  than 
in  any  other  one  branch  of  science  and  a  preliminary  definition 
of  them  would  from  their  mere  number  tend  to  confusion  rather 
than  to  clearness;  moreover,  an  accurate  conception  of  some  of 
them  requires  more  or  less  knowledge  of  certain  electrical  principles 
and  relations,  therefore,  it  is  found  best  to  reserve  these  definitions 
until,  in  the  development  of  the  subject,  the  necessity  for  their 
use  arises. 

3.  Fundamental  Units. — There  are,  however,  certain  units  of 
general  application  in  all  sciences  and  of  these  it  is  well  to  have 
from  the  beginning  a  definite  conception.    Such  are  the  so-called 
"fundamental"  units  of  length,  mass  and  time  and  some  others 
derived  from  these. 

We  may,  in  a  sense,  regard  the  unit  of  length  alone  as  the  fun- 
damental unit  for  it  is  possible  to  define  all  the  others  more  or  less 
directly  by  reference  to  length.  Thus,  the  unit  of  mass  may  be 
defined  as  the  mass  of  water  under  certain  conditions  contained 
in  a  cube  of  certain  dimensions,  the  unit  of  time  in  terms  of  the 
period  of  oscillation  at  a  certain  locality  of  a  pendulum  of  a  cer- 
tain length,  the  unit  of  heat  in  terms  of  the  linear  expansion  of 
mercury,  etc. 

1 


2  ELEMENTS  :OF  ELECTRICITY. 

The  term  "fundamental"  is  however  applied  to  the  units  of 
length,  mass  and  time  because  in  addition  to  the  simpler  derived 
units  of  area,  volume  and  weight,  it  is  possible,  as  will  be  shown 
below,  to  express  all  such  dynamical  quantities  as  velocity,  force, 
work,  etc.,  in  terms  of  these  units.  This  does  not  mean  that  there 
is  one  universal  fundamental  unit  of  length  or  of  mass  or  of  time. 
The  units  are  chosen  arbitrarily,  but  once  having  been  selected 
the  system  of  derived  units  follows. 

4.  Standard  of  Length. — The  desirability  of  having  a  single 
unvarying  standard  of  length,  one  that  could  be  reproduced  should 
existing  standards  be  destroyed,  has  long  been  evident.     It  has 
been  proposed  to  take  as  such  standard  the  length  of  the  simple 
seconds  pendulum  at  the  sea  level  at  some  definite  locality.    This 
is  about  39.14  inches. 

The  French  government  caused  to  be  made  most  accurate  meas- 
urements of  several  meridian  arcs  of  the  earth's  surface  whence 
was  calculated  the  length  of  the  meridian  quadrant  through  Paris 
and  one  ten-millionth  part  of  this  quadrant  (about  40  inches) 
was  adopted  as  the  measure  of  length  and  hence  called  the  meter. 
A  standard  meter  of  platinum  was  made  and  is  preserved  in 
France.  It  is  now  known  that  an  error  was  made  in  the  deter- 
mination of  the  length  of  the  quadrant  and  that  it  is  some  880 
meters  longer,  so  that  practically  the  meter  is  the  length  of  the 
platinum  bar,  the  "metre  des  archives"  of  France.  Its  length  is 
39.37+  inches. 

5.  Need  of  Multiples  and  Submultiples. — Although  it  would 
seem  that  there  should  be  but  one  unit  for  any  one  kind  of  quan- 
tity, as  a  matter  of  fact  this  is  not  the  case.    The  need  of  more 
than  one  arises  mainly  from  the  fact  that  the  average  human 
mind  can  not  form  a  direct  concrete  conception  of  a  quantity 
expressed  by  more  than  three  figures.     For  example,  should  a 
person  say  that  he  had  walked  63,360  inches  we  have  no  precise 
image  of  the  actual  distance,  and  even  when  expressed  as  5280 
feet  we  involuntarily  translate  into  the  next  higher  unit;  but  when 
he  says  that  he  has  walked  one  mile  we  get  a  definite  idea.    In  the 
other  direction,  to  speak  of  an  object  as  one  63,360th  of  a  mile  thick 
is  almost  meaningless  but  one  inch  conveys  the  exact  impression. 
Therefore  in  practical  affairs  we  require  large  units  to  measure 
large  quantities  and  small  units  to  measure  small  quantities. 


INTRODUCTORY. 


6.  The  Metric  System.— It  is  not  necessary  to  explain  here 
the  advantages  of  the  metric  or  decimal  system.    The  following 
table  of  English  measures  of  length — 

3  barleycorns  make  an  inch 
12  inches  make  a  foot 

3  feet  make  a  yard 
1760  yards  make  a  mile 

and  the  fact  that  besides  these  we  have  the  line,  the  hand,  the 
ell,  the  fathom,  the  rod,  perch  or  pole,  the  chain,  the  furlong,  the 
geographical  mile,  the  nautical  mile,  the  knot,  the  league,  etc., 
between  which  in  general  no  interrelation  exists,  are  sufficient  to 
show  how  illogical  is  our  system.  This  is  brought  out  all  the 
more  forcibly  when  we  attempt  to  pass  from  one  of  these  units  to 
another  or  to  make  a  calculation  in  which  several  are  involved  or 
to  pass  from  linear  dimensions  to  measures  of  capacity. 

The  metric  system  has  by  act  of  Congress  been  formally 
legalized  for  use  in  this  country,  but  in  spite  of  its  advantages  its. 
introduction  into  every-day  affairs  has  made  but  little  progress 
and  its  employment  is  confined  mainly  to  the  sciences. 

7.  Unit  of  Length   Selected   by   Electricians. — The  meter  is. 
subdivided  into  ten  parts,  decimeters,  a  unit  but  little  used,  and 
these  are  again  subdivided  into  ten  parts,  centimeters.    This  last 


cubic  cm. 


centimeter  scale 
Fig.  1. 


unit,  a  length  only  very  little  less  than  four-tenths  of  an  inch,  is 
adopted  by  electricians  as  their  fundamental  unit  of  length.  The 
selection  of  the  centimeter  rather  than  the  meter  was  largely  in- 
flu^nced  by  the  fact  that  the  cubic  centimeter  of  water  weighs  one 
gram  and  consequently  to  determine  the  specific  gravity  of  a  sub- 
stance it  is  only  necessary  to  obtain  the  weight  of  a  cubic  centi- 
meter of  it  in  grams. 

8.  The  Unit  of  Mass. — Mass  and  weight  should  not  be  con- 
fused. The  mass  of  a  body  is  the  quantity  of  matter  which  it 
contains  and  is  invariable  but  its  weight  varies  as  it  changes  its 
position  with  respect  to  the  earth's  center  of  gravity.  Neverthe- 


4  ELEMENTS  OF  ELECTRICITY. 

less,  the  masses  of  similar  bodies  under  like  conditions  are  propor- 
tional to  their  weights  and  practically  we  compare  masses  by 
comparing  their  weights. 

In  the  metric  system  the  unit  of  mass  is  the  mass  of  a  cubic 
decimeter  of  distilled  water  at  its  maximum  density,  4°  C.  The 
weight  of  this,  the  kilogram  (about  2.2  pounds),  is  the  French 
industrial  unit  of  weight  and  is  perpetuated  in  a  platinum  standard. 

The  kilogram  being  inconveniently  large  for  their  purposes, 
electricians  and  other  physicists  have  taken  as  their  fundamental 
unit  the  gram,  the  mass  of  a  cubic  centimeter  of  distilled  water 
at  4°  C.  Our  five-cent  nickel  coin  weighs  about  5.26  grams. 

9.  The  Unit  of  Time. — The  unit  of  time  used  by  electricians 
is  the  mean  solar  second.    As  the  earth's  orbit  is  not  circular  but 
elliptical,  the  velocity  of  the  earth  varies  at  various  points  and 
the  apparent  solar  day,  or  the  interval  of  time  between  two  suc- 
cessive passages  of  the  sun  across  the  meridian,  also  varies.    The 
average  throughout  the  year  of  these  apparent  solar  days  is  taken 
as  the  mean  solar  day  and  this  is  considered  as  composed  of  24 
hours  of  60  minutes  of  60  seconds,  or  as  divided  into  86,400  mean 
solar  seconds. 

10.  The  C.  G.  S.  System. — The  centimeter,  the  gram  and  the 
second  were  recommended  as  fundamental  units  by  a  committee 
of  the  British  Association  in  1873  and  were  formally  adopted  by 
the  International  Congress  of  Electricians  in  Paris  in  September, 
1881.    From  these  are  obtained  the  various  derived  units  and  the 
system  is  therefore  usually  referred  to  as  the  "C.  G.  S.  system." 

11.  Absolute  Units. — Derived  units  are  of  two  classes,  absolute 
and  practical.     The  term  absolute,  first  used  in  this  connection 
by  Gauss,  is  applied  to  those  units  which  are  derived  from  the 
fundamental  units  of  the  system,  depend  upon  them  absolutely 
and  exclusively  and  are  independent  of  the  force  of  gravity  or  of 
any  instrument  or  apparatus  or  of  any  arbitrary  weight  or  size 
of  any  arbitrary  material.    Many  of  the  absolute  units  are  incon- 
veniently small,  others  are  inconveniently  large,  and  this  gives 
rise  to  the  practical  units  which  more  nearly  fulfill  the  require- 
ments of  the  practical  electrician. 

Area. — The  absolute  unit  of  area  is  the  square  centimeter. 
Volume. — The  absolute  unit  of  volume  is  the  cubic  centimeter. 


INTRODUCTORY.  5 

Velocity. — The  absolute  unit  of  velocity  is  the  velocity  of  a 
body  which  moves  at  the  rate  of  one  centimeter  per  second.  The 
practical  unit  in  the  metric  system  is  one  meter  per  second  and  in 
the  English  system  one  foot  per  second. 

Acceleration.— Acceleration  is  the  rate  of  change  of  velocity  and 
the  absolute  unit  is  the  acceleration  of  a  body  which  changes  its 
velocity  one  centimeter  per  second. 

Force. — Force  is  measured  by  the  acceleration  which  it  imparts 
to  a  given  mass.  The  absolute  unit,  the  dyne,  is  that  force  which 
acting  for  one  second  upon  a  mass  of  one  gram  causes  its  velocity 
to  change  one  centimeter  per  second.  If  the  mass  starts  torn  rest, 
at  the  end  of  the  first  second  it  will  have  acquired  a  velocity  of 
one  centimeter  per  second;  if  the  mass  be  moving  its  velocity  will 
be  accelerated  or  retarded  one  centimeter  per  second.  The  dyne 
is  a  very  small  force.  The  weight  of  one  gram  corresponds  to  981 
dynes,  that  of  our  five-cent  piece  to  about  5160  and  the  head  of 
the  average  pin  to  about  15.  The  practical  unit  in  the  English 
system  is  the  pound,  which  is  nearly  445,000  dynes. 

Work. — Work  is  the  expenditure  of  energy  in  overcoming  a 
resistance  over  a  path.  The  absolute  unit  of  work,  the  erg,  is  the 
work  performed  in  pushing  or  pulling  against  a  force  of  one  dyne 
over  a  path  of  one  centimeter.  The  erg  is  a  very  small  unit.  The 
English  practical  unit,  the  foot-pound,  or  the  work  performed  in 
lifting  a  weight  of  one  pound  for  one  foot  against  the  force  of 
gravity,  is  in  round  numbers  13,560,000  ergs. 

Energy. — Energy  is  the  capacity  of  a  body  to  do  work  and 
hence  is  measured  by  the  work  which  it  can  do,  therefore,  the 
absolute  unit  of  energy  is  also  the  erg. 

Heat. — The  absolute  unit  of  heat,  the  small  calorie,  is  the 
amount  of  heat  required  to  raise  the  temperature  of  one  gram  of 
water  from  0°  to  1°  on  the  Centigrade  scale.  According  to  the 
latest  determination  of  the  mechanical  equivalent  of  heat  it  re- 
quires an  expenditure  of  1402  foot-pounds  to  raise  one  pound  of 
water  from  0°  to  1°  C.  The  small  calorie  is  therefore  equivalent 
to  42,000,000  ergs. 

In  the  C.  G.  S.  system  the  practical  units  are  some  power  of 
ten  times  the  absolute  units  and  these  practical  units  have  been 
named  after  distinguished  electricians. 


6  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  2. 
ELECTRICITY. 

12.  Origin  of  the  Name.— Among  the  stones  esteemed  pre- 
cious by  the  ancients  was  amber  to  which  the  Greeks  applied  the 
name  "elektron."  This  substance,  which  is  now  known  to  be  a 
fossil  resin,  is  found  in  various  localities  but  especially  along  the 
shores  of  the  Baltic  where  it  is  cast  up  on  the  beaches  after  storms. 
It  was  prized  On  account  of  its  golden  yellow  color  and  luster  and 
also  because  of  certain  talismanic  properties  attributed  to  it.  It 
is  quite  soft  and  easily  fashioned  into  beads  which  can  be  given  a 
high  polish  by  rubbing  with  a  dry,  woolen  cloth.  The  workmen 
engaged  in  preparing  these  soon  noticed  that  upon  rubbing  a  piece 
it  acquired  a  property  which  it  had  not  before  possessed,  that  is, 
it  attracted  to  itself  light  substances  such  as  particles  of  lint  and 
dust,  bits  of  straw,  feathers,  etc.  This  property  quickly  died 
away  but  could  be  revived  by  renewed  rubbing.  These  obser- 
vations are  recorded  by  writers  of  2500  years  ago  who,  as  was 
usual  in  such  cases,  fell  back  upon  the  supernatural  for  an  explana- 
tion and  ascribed  to  the  substance  certain  mystical  qualities. 

For  over  two  thousand  years  such  remained  the  state  of  knowl- 
edge. During  the  reign  of  Queen  Elizabeth  a  certain  Doctor 
Gilbert,  an  Englishman,  carried  out  a  very  remarkable  series  of 
experiments  and  observations  upon  the  then  vaguely  known 
properties  of  magnets,  and  as  allied  to  magnets  investigated  other 
bodies  in  which  powers  of  attraction  could  be  produced.  He  dis- 
covered that  this  property  was  by  no  means  confined  to  amber 
and  in  Chapter  II,  Book  Second,  of  his  work,  De  Magnete,  Mag- 
neticisque  Corporibus  (On  the  Magnet  and  Magnetic  Bodies), 
published  in  1600  he  enumerates  a  list  of  substances,  mainly 
vitreous  or  crystalline  and  resinous  or  resinoid,  which  possess  it. 
He  mentions  among  others  the  diamond,  sapphire,  opal,  varieties 
of  rock  crystal,  glass,  fluor  spar,  rock  salt,  mica,  sealing  wax,  resin, 
jet,  sulphur,  etc.,  and  to  all  these  bodies  in  which,  like  amber  or 
elektron,  the  power  of  attraction  could  be  produced  by  rubbing 
he  applied  the  term  "electrics."  From  this  it  was  an  easy  transi- 


INT  ROD  UC  TOR  Y.  7 

tion  to  the  word  "electricity"  applied  both  to  the  study  or  science 
and  to  the  agent  itself. 

13.  Electricity. — At  the  very  outset  we  are  compelled  to  admit 
that  we  do  not  know  what  electricity  is.    It  is  not  matter  since  it 
is  devoid  of  physical  dimensions  and  weight;  yet  in  its  production, 
transmission  and  manifestation  it  must  always  be  associated  with 
matter.    Mechanical  or  chemical  energy  applied  to  matter  at  one 
point  may  be  used  to  produce  electricity  which  may  be  trans- 
mitted to  some  other  point  and  there  used  to  reproduce  energy  of 
either  kind.     Its  great  value  in  the  industrial  world  consists  in 
this  very  ability  to  transfer  energy  instantly  to  great  distances 
and  to  deliver  it  with  minimum  loss. 

Fortunately  for  our  purposes  a  theory  is  not  essential,  for 
although  our  knowledge  of  the  agent,  electricity,  is  restricted  to 
the  various  phenomena  which  it  produces,  the  laws  under  which 
it  operates  are  definite  and  well  known  and  under  any  given  set 
of  conditions  we  are  able  to  predict  what  the  electrical  outcome 
will  be.  The  study  of  electricity  which  we  are  about  to  take  up  is 
therefore  but  an  orderly  and  logical  presentation  of  these  phe- 
nomena and  of  the  laws  which  govern  them. 

14.  Divisions  of  the  Subject. — Like   any   other  science  elec- 
tricity can  not  be  studied  as  a  whole  but  must  be  separated  into 
subdivisions,  more  or  less  artificial,  and  these  subdivisions  taken 
in  such  order  and  detail  as  may  appear  most  suited  to  the  develop- 
menfof  the  subject  while  at  the  same  time  avoiding  undue  repeti- 
tion or  presentation  of  facts  involving  anticipation  of  principles 
not  yet  explained. 

It  is  customary  to  consider  electricity  under  four  heads  cor- 
responding to  the  four  conditions  under  which  its  effects  are 
usually  observed. 

1st,  Electricity  may  exist  as  a  motionless  charge  upon  bodies. 
If  a  wooden  ball  at  the  end  of  a  stiff  wire  be  dipped  under  water 
and  then  withdrawn  it  will  be  covered  with  a  film  of  moisture  and 
this  is  very  roughly  analogous  to  the  charge  of  electricity  which 
may  be  imparted  to  a  metal  ball  supported  upon  a  glass  stem. 
This  is  termed  stationary  or  static  electricity. 

2nd,  With  a  suitable  path  to  direct  it,  electricity  may  flow  in  a 
constant  stream.  This  is  current  electricity. 


8  ELEMENTS  OF  ELECTRICITY. 

3rd,  Associated  with  certain  metals,  mainly  iron,  its  oxides  and 
steel,  there  are  met  manifestations,  termed  magnetic,  which  take 
the  form  of  forces  traversing  the  metal,  emerging  at  one  end, 
following  a  curved  path  and  re-entering  at  the  other  end.  An 
electric  current  is  surrounded  by  similar  whirling  forces;  electricity 
may  be  made  to  produce  magnetic  effects  and  conversely  from 
magnetic  forces  electricity  may  be  produced.  A  third  division 
is  therefore  magnetism. 

4th,  Finally,  typically  in  the  case  of  wireless  telegraphy,  the 
electricity  is  not  in  the  form  of  a  charge  nor  of  a  current  but  is 
transmitted  through  space  by  means  of  intermittent  oscillations 
or  waves. 

From  a  practical  standpoint,  the  least  important  of  the  above 
is  the  static  electricity  but  it  is  now  to  be  considered  because  of 
its  historical  interest,  its  development  being  chronologically  the 
first  and  associated  with  the  names  of  many  noted  scientists, 
among  whom  our  Franklin  played  a  prominent  part.  It  also 
enables  us  to  present  in  a  simple  manner  certain  useful  principles 
and  conceptions  and  thus  serves  as  a  stepping-stone  to  what 
follows. 


STATIC  ELECTRICITY. 

PART  I. 
STATIC  ELECTRICITY. 


CHAPTER  3. 

ELECTRIC   ATTRACTION    AND   REPULSION. 

15.  Electric  Attraction. — If  on  a  dry  day  a  rod  of  glass  or  of 
resin  or  of  some  resinoid  substance  such  as  amber,  sealing  wax, 
vulcanized  rubber,  sulphur,  celluloid,  etc.,  be  rubbed  with  a  piece 


Fig.  2. 


of  fur  or  woolen  cloth  (wool  is  fur)  and  then  held  immediately 
above  small  particles  of  light  substances  such  as  bits  of  tissue 
paper,  feathers,  straw  or  chaff,  the  particles  will  leap  up  and  cling 
to  the  rod.  In  the  case  of  a  glass  rod  the  effect  is  more  pronounced 
if  it  be  rubbed  with  silk  instead  of  with  fur.  The  rod  is  said  to  be 
electrified  and  the  state  persists  for  some  time  in  dry  weather  but 
disappears  quickly  if  it  be  damp.  The  electrification  is  instantly 
lost  if  the  rod  be  rubbed  over  its  entire  surface  with  the  hand,  or 
if  it  be  dipped  into  water  or  passed  quickly  through  a  flame. 

If  an  excited  or  electrified  rod  be  held  above  a  small  block  of 
wood  no  appreciable  effect  will  be  produced,  but  if  the  block  be 
cut  up  into  fine  shavings  they  will  be  readily  attracted.  Although 
the  block  is  attracted  the  electric  force  is  too  feeble  to  move  it  as 
a  whole  but  easily  moves  the  light  pieces.  In  experimenting  with 
electric  attraction,  on  account  of  this  feebleness  it  is  customary  to 


10  ELEMENTS  OF  ELECTRICITY. 

use  balls  of  pith,  a  substance  which  combines  bulk  with  extreme 
lightness. 

16.  Electrified  Bodies  Attract  Non-Electrified.— An  electrified 
body  attracts  all  non-electrified,  including  the  metals,  liquids,  etc. 
Gilbert,  who  made  this  discovery,  excepted  only  such  bodies  as 
are  "afire  or  flaming  or  the  thinnest  air"  and  devised  a  piece  of 
apparatus,  a  versorium  (rotating  needle,  revolving  pointer),  by 

which  this  may  be  shown.  Light 
needles  of  various  substances  were 
made  and  like  compass  needles 
balanced  free  to  turn  upon  a  pivot. 
If  these  be  approached  by  an  electri- 
fied body  they  will  turn  towards  it. 
If  an  electrified  piece  of  amber  be 

held  above  a  spherical  globule  of  water  the  globule  will  assume  a 
conical  shape  as  if  reaching  up  to  the  amber,  so  also  the  dense 
smoke  from  a  recently  extinguished  candle  will  be  attracted. 

17.  Electrified  Bodies  are  Attracted  by  Non-Electrified.— The 
attraction  between  an  electrified  body  and  a  non-electrified  is 
mutual.     This  follows  necessarily  from -a  fundamental  principle 
of  mechanics  but  may  easily  be  shown  by  suspending  by  a  fine 
thread  an  electrified  rod  so  as  to  turn  horizontally  like  Gilbert's 
versorium.    If  a  non-electrified  body  be  held  near,  the  rod  will 
be  attracted  and  turn  towards  it. 

18.  Electric  Charge. — If  two  rods  of  sealing  wax  be  rubbed 
with  a  woolen  cloth  they  each  become  electrified.     If  they  be 
rubbed  one  against  the  other  no  effect  is  produced.     Finally,  if 
one  be  electrified  by  rubbing  and  then  the  second  be  touched  by 
the  first,  the  second  will  be  found  to  be  slightly  electrified.     In 
other  words,  the  electrified  rod  communicates  a  portion  of  its 
electrification  to  the  non-electrified.    The  electrification  upon  a 
body  is  spoken  of  as  a  charge;  an  electrified  body  is  said  to  be 
charged;  and  when  the  electrification  is  withdrawn  it  is  said  to  be 
discharged. 

19.  Conductors  and  Non- Conductors. — In  1729  Stephen  Gray, 
experimenting  with  electric  attraction,  used,  instead  of  a  glass 
rod,  a  tube  into  the  open  ends  of  which  he  had  stuck  corks  to  keep 
out  the  dust.    Upon  rubbing  the  glass  tube  he  was  surprised  to 
find  that  the  corks  which  had  not  been  rubbed  had  nevertheless 


STATIC  ELECTRICITY. 


11 


acquired  the  property  of  attraction  as  if  the  charge  generated 
upon  the  glass  had  spread  upon  them.  To  test  this  further  he 
inserted  in  the  corks  long  wands  of  wood  or  metal  terminating  in 
balls  and  found  that  when  the  glass  was  rubbed  the  balls  attracted 
light  objects.  In  place  of  the  wands  he  next  tried  cords  and  wires 
by  which  he  suspended  a  ball  from  a  glass  tube  held  in  a  balcony 
above  and  found  that  the  ball  became  electrified  as  soon  as  the 
tube  was  rubbed.  Wishing  to  continue  this  experiment  at  a 
greater  distance  than  could  be  obtained  from  his  balcony  he  was 
obliged  to  stretch  his  cord  hori- 
zontally, and  to  keep  it  clear  of 
the  ground  he  hung  it  up  at  inter- 
vals by  bits  of  thread  attached 
to  nails  in  a  post.  Under  these 
conditions  he  was  unable  to  elec- 
trify the  ball  and  he  surmised 
correctly  that  the  charge  had 
escaped  by  way  of  the  suspending 
threads.  A  friend  who  was  assist- 
ing him  suggested  that  they  use 
a  smaller  thread  which  would 
give  a  smaller  path  by  which  the 
charge  could  escape  and  a  spool 
of  silk  being  at  hand  it  was  tried 
with  the  result  that  he  was  able 
to  electrify  the  ball  at  greater  and 
greater  distances  up  to  as  far  as 
765  feet.  Finally,  the  silk  thread 
breaking  under  the  strain,  he 
tried  a  fine  wire,  even  smaller  than 
the  silk,  but  was  unable  to  elec- 
trify the  ball  and  now  perceived 
for  the  first  time  that  the  escape 
of  the  charge  depended  not  upon 
the  size  of  the  suspensions  but 
upon  the  material  of  which  they 
were  made.  As  a  result  of  a  con- 


Fig.  4. 


tinuation  of  these  experiments  he  was  enabled  to  arrange  all  bodies 
in  two  classes,  one  which  transmitted  electricity  to  a  distance  and 
which  he  called  conductors,  the  other  preventing  this  transmission 


12  ELEMENTS  OF   ELECTRICITY. 

and  called  non-conductors  or  insulators.  In  the  light  of  modern 
investigation  we  now  know  that  there  is  no  strict  dividing  line 
between  the  two  and  that  there  is  no  such  thing  as  a  perfect  con- 
ductor nor  a  perfect  insulator  but  that  all  bodies  offer  resistance 
to  the  passage  of  electricity,  those  that  offer  but  little  being 
termed  conductors,  those  that  offer  a  great  deal  being  termed 
non-conductors.  Joubert  concisely  defines  good  conductors  as 
those  bodies  which  when  electrified  at  one  point  are  immediately 
found  to  be  electrified  all  over. 

20.  Table  of  Conductors  and  Non- Conductors. — In  the  follow- 
ing list  the  commoner  conductors,  partial  conductors  and  non- 
conductors are  arranged  in  order  of  their  conductivity  beginning 
with  silver,  the  best  conductor,  and  ending  with  air,  the  poorest 
conductor  (or  best  non-conductor).  This  arrangement  is  not 
rigorously  exact  since  relative  conductivity  may  vary  with  change 
of  temperature  and  other  circumstances: 

Good  Conductors:  Non-Conductors: 

Silver  Slate 

Copper  Oils 

Aluminum  Porcelain 

Brass  Leather 

Platinum  Paper 

Iron  Wool 

Lead  Silk 

Mercury  Resin 

Fair  Conductors:  Rubber 

Compact  carbon  Shellac 

Acid  solutions  Vulcanized  rubber 

Salt  solutions  Mica 

Living  plants  Paraffine 

Damp  earth  Glass 

Partial  Conductors:  Air 
Water 

Animal  bodies 
Flame 
Cotton 
Woods 
Marble 

The  foregoing  explains  why  an  electrified  body  is  discharged 
when  rubbed  with  the  hand  or  dipped  into  water  or  passed  through 
a  flame,  also  why,  as  Gilbert  discovered,  damp  weather  is  unfavor- 
able for  the  production  of  electrification. 


STATIC  ELECTRICITY. 


13 


21.  All   Bodies   Susceptible  of  Electrification. — In  contradis- 
tinction to  his  electrics  Gilbert  designated  as  non-electrics  those 
bodies  in  which  he  was  unable  to  produce  electrical  attraction  by 
friction.    Among  these  he  enumerates  various  flints  and  agates, 
marble,  bone,  ivory,  the  metals,  the  lodestone,  the  human  body, 
etc.    We  now  know  that  he  was  in  error  in  supposing  that  they 
could  not  be  electrified.     Examination  of  the  table  above  will 
show  that  his  electrics  are  all  non-conductors  and  his  non-electrics 
are  all  conductors.     When  he  attempted  to  electrify  a  piece  of 
metal  the  charge  upon  it  was  instantly  conducted  away.    If  the 
metal  be  attached  to  a  glass  handle  it  is  readily  electrified.    If  a 
person  stand  upon  a  glass-legged  stool  or  upon  a  cake  of  resin  or 
be  suspended  by  silk  cords  and  then  be  touched  by  an  electrified 
glass  rod  or  stroked  by  a  piece  of  fur  he  will  be  strongly  electrified, 
small  light  particles  will  fly  to  him  as  to  the  electrified  amber  and 
if  a  second  person  attempt  to  touch  him,  just  when  the  distance 
between  the  outstretched  hand  and  the  electrified  person  becomes 
very  small  a  faint  snapping  noise  will  be  heard  and  both  persons 
will  perceive  a  slight  pricking  sensation.     In  the  dark  it  will  be 
seen  that  this  noise  accompanies  a  spark.    All  bodies  if  properly 
insulated  so_that  the  charge  upon  them  can  not  escape  may  be 
electrified. 

22.  Electric  Repulsion. — Reverting  to  the  first  experiment  in 
electric  attraction  (Par.  15),  if 

the  electrified  rod  with  the  par- 
ticles adhering  to  it  be  observed 
for  a  brief  interval,  the  par- 
ticles will  be  seen  to  leap  or 
dart  away  from  the  rod  as  if 
shot  away  by  a  repelling  force. 
This  repulsion  does  not  take 
place  until  after  the  particles 
have  been  in  contact  with  the 
electrified  rod.  To  exhibit  this 
better,  use  is  made  of  the  so- 
called  electric  pendulum,  a  pith 
ball  suspended  by  a  fine  silk 
thread  (Fig.  5).  If  the  ball  be 
approached  by  an  electrified  rod 


Fig.  5. 
it  will  fly  to  the  rod  and  after  a  short  contact  will  be  repelled. 


14  ELEMENTS  OF  ELECTRICITY. 

If  the  rod  be  moved  in  pursuit  the  ball  will  continue  to  move 
away  avoiding  the  rod.  The  ball  is  now  charged,  as  may  be 
shown  by  its  being  attracted  by  any  non-electrified  body  held 
near  it;  the  repulsion  must  therefore  be  due  to  the  charge  which  it 
acquired  by  its  contact  with  the  rod. 

23.  Two  Kinds  of  Electrification.— If  the  pith  ball  of  an  electric 
pendulum  be  approached  by  a  stick  of  sealing  wax  which  has  been 
rubbed  with  fur,  it  will  first  be  attracted  and  after  contact  will  be 
repelled.    Similarly,  if  it  be  approached  by  a  glass  rod  which  has 
been  rubbed  with  silk,  it  will  be  attracted  until  contact  is  made  and 
thereafter  repelled.    But  the  strange  part  is  that  the  ball  repelled 
by  the  electrified  sealing  wax  is  attracted  by  the  electrified  glass 
and  the  ball  repelled  by  the  glass  is  attracted  by  the  sealing  wax. 
The  electrification  produced  upon  the  glass  must  therefore  be  dif- 
ferent from  that  produced  upon  the  sealing  wax.    Dufay,  who  in 
1733  made  this  discovery,  designated  these  by  the  terms  vitreous 
and  resinous,  vitreous  being   that  produced   by  rubbing  glass 
with  silk  and  resinous  that  by  rubbing  sealing  wax  with  fur.     It 
has  since  been  discovered  that  the  kind  of  electricity  produced 
does  not  depend  entirely  upon  the  material  of  the  body  rubbed 
but  also  upon  that  of  the  rubber  and  moreover  varies  in  a  sur- 
prising manner  with  the  polish,  the  temperature  and  even  the 
color  of  the  body  rubbed.    Glass  rubbed  by  silk  is  vitreously 
electrified  but  if  it  be  rubbed  by  fur  it  is  resinously  electrified. 
It  is  possible  to  arrange  a  list  of  substances  so  that  any  one 
body  in  it  is  vitreously  electrified  when  rubbed  by  any  other 
below  it  on  the  list.    The  following  is  such  a  list: — Fur,  glass, 
flannel,  feathers,   silk,  paper,   wax,  metals,  vulcanized  rubber, 
celluloid. 

In  view  of  the  above  it  is  better,  for  reasons  given  in  Par.  27,  to 
follow  Franklin  and  employ  the  terms  positive  and  negative,  the 
vitreous  being  positive,  the  resinous  negative. 

24.  Like  Charges  Repel,  Unlike  Attract. — If  two  pith  balls  sus- 
pended side  by  side  by  separate  silk  threads  (Fig.  6)  be  approached 
by  an  electrified  rod  of  glass  or  of  sealing  wax  they  will  both  be 
attracted  to  the  rod  and,  as  soon  as  they  have  touched  it,  will  be 
repelled,  but  not  only  this,  they  will  repel  each  other  and  no 
longer  hang  side  by  side  but  will  diverge  and  stand  apart.    If  two 
separate  pendulums  be  used  and  the  pith  ball  of  one  be  charged 


STATIC  ELECTRICITY. 


15 


Fig.  6. 


from  a  glass  rod,  the  other  from  a  rod  of  sealing  wax,  the  balls 
will  attract  each  other.    We  therefore  see 
that  bodies  charged  with  like  electricity  repel 
each  other;  those  charged  with  unlike  elec- 
tricity attract  each  other. 

25.  Electroscopes. — Instruments  for  deter- 
mining (a)  whether  a  body  is  charged  or  not 
and  (b)  the  nature  of  the  charge  are  called 
electroscopes.    The  simplest  form  of  an  elec- 
troscope is  Gilbert's  versorium  described  in 
Par.  16.    The  electric  pendulum  is  frequently 
used  as  an  electroscope.    If  the  pith  ball  after 
being  touched  by  the  hand  is  attracted  by 

the  body  being  investigated,  the  body  is  charged.  After  we  have 
in  this  way  ascertained  that  the  body  is  charged  we  next  deter- 
mine the  nature  of  the  charge  by  charging  the  pith  ball,  say  posi- 
tively, or  from  a  glass  rod  which  has  been  rubbed  by  silk,  after 
which  when  held  near  the  body  it  will  be  repelled  if  the  latter  be 
charged  positively  and  attracted  if  it  be  charged  negatively. 

The  large  insulated  metal  conductors,  used  with  certain  electrical 
machines  to  be  described  later,  often  have  attached  to  them  as 
charge  indicators  small  electric  pendulums  which  differ  from  the 
one  already  described  in  that  the  support  is  a  brass  rod  and  that 
the  pith  ball  is  suspended  by  a  linen  or  cotton  thread  or  by  a  very 
slender  metal  filament  instead  of  by  a  silk  thread.  When  the  con- 
ductor is  charged  the  pith  ball  becomes  charged  through  the 
suspending  thread  and  is  repelled  and  stands  out  at  an  angle  from 
the  vertical  brass  support.  Since  the  greater  the  charge  the 
greater  the  repulsion  and  the  greater  the  angle  at  which  the  pith 
ball  stands,  this  instrument  indicates  roughly  the  relative  amount 
of  the  charge. 

The  gold-leaf  electroscope,  a  much  more  sensitive  form,  is  de- 
scribed further  on  (Par.  34). 

26.  Simultaneous  Production  of  Equal  Amounts  of  Both  Kinds 
of   Electricity. — In  producing  electricity  by  friction  the  body 
rubbed  acquires  a  certain  kind  of  charge  and  the  rubber  acquires 
the  other  kind;  thus  in  rubbing  a  glass  rod  with  silk  the  rod  is 
charged  with  vitreous  or  positive  electricity  and  the  silk  can  be 
shown  to  have  a  resinous  or  negative  charge.     Furthermore,  as 


16  ELEMENTS  OF  ELECTRICITY. 

may  be  shown  in  several  ways,  the  amounts  of  the  two  kinds  are 
exactly  equal.  If  two  substances  are  rubbed  together  and -acquire 
opposite  charges  and  their  charges  be  imparted  successively  to  a 
third  body  the  third  body  will  not  be  electrified.  If  a  disc  of  glass 
and  one  covered  with  silk,  both  being  mounted  on  glass  handles,  be 
rubbed  together  they  will  each  separately  attract  pith  balls  but 
when  placed  together  will  have  no  effect,  the  charge  on  the  one 
exactly  counterbalancing  or  neutralizing  that  on  the  other. 

27.  Theories  of  Electricity. — Two  theories  were  advanced  to 
account  for  the  above  phenomena.  The  first  is  Symmer's  Two 
Fluid  Theory.  According  to  this  there  exist  in  all  bodies  two 
electrical  fluids  of  opposite  kinds  but  in  exact  balance,  thus  neutral- 
izing each  other.  When  a  body  is  excited  by  friction  this  balance 
is  disturbed  and  one  of  the  fluids  is  drawn  off  upon  the  rubber 
leaving  the  remaining  fluid  unbalanced  and  in  excess.  In  this 
country  the  theory  most  generally  accepted  is  Franklin's  Single 
Fluid  Theory.  In  brief  this  is  to  the  effect  that  all  bodies  in  their 
natural  state  are  charged  with  a  certain  quantity  of  electricity, 
in  each  body  this  quantity  being  of  definite  amount.  When  two 
bodies  are  rubbed  together  one  parts  with  a  portion  of  its  electric- 
ity which  is  appropriated  by  the  other.  The  latter  then  has  more 
than  its  normal  share  and  is  positively  electrified;  the  former  has 
less  and  is  negatively  electrified.  It  is  proper  to  state  here  that 
although  we  do  not  know  what  electricity  is,  we  do  know  that  it 
is  not  a  fluid  yet  we  retain  the  term  for  convenience,  and  that 
although  we  speak  of  bodies  being  positively  or  negatively  elec- 
trified we  really  do  not  know  which  has  the  greater  charge  and 
the  terms  are  used  purely  in  a  conventional  sense,  just  as  in 
analytical  geometry  distances  to  the  right  of  the  vertical  axis  are 
by  convention  considered  positive  and  those  to  the  left  negative. 
Finally,  no  satisfactory  explanation  is  given  why  bodies  should 
acquire  unlike  charges  by  friction.  The  amount  of  electrification 
is  not  proportional  to  the  amount  of  mechanical  energy  spent  in 
friction,  since  it  is  immaterial  whether  the  friction  be  of  the  ordi- 
nary kind  or  be  rolling,  but  it  is  proportional  to  the  amount  spent 
in  pulling  apart  two  bodies  held  together  by  the  mutual  attraction 
due  to  their  opposite  electrical  states. 


STATIC  ELECTRICITY. 


17 


CHAPTER  4. 

ELECTROSTATIC   INDUCTION. 

28.  Electrification  by  Influence. — In  Fig.  7,  A  represents  a 
metallic  ball  attached  to  a  stand  by  a  glass  stem  and  B  a  metallic 
cylinder  similarly  mounted  and  carrying  on  its  under  side  a  series 
of  pairs  of  pith  balls  hanging  from  linen  threads.  So  far  as  elec- 
trical results  are  concerned,  it  is  immaterial  whether  the  ball 
and  cylinder  be  solid  or  hollow.  They  may  even  be  of  wood 
covered  with  tjn-foil  or  gilded  but  are  usually  made  of  thin  brass. 


C 


A    A 


B 


Fig.  7. 

If  now  the  ball  A,  while  at  some  distance  from  B,  be  given  a  charge, 
say  positive,  and  then  be  moved  up  towards  B,  the  pith  balls 
beneath  B  will  be  observed  to  diverge  indicating  that  B  is  charged. 
Since  A  has  not  touched  B  and  since  the  same  effect  is  produced 
when  a  sheet  of  glass  is  interposed  between  A  and  B  and,  finally, 
since  it  can  be  shown  that  the  charge  upon  A  is  undiminished,  the 
charge  upon  B  could  not  have  been  communicated  from  A  but 
must  have  been  induced  or  produced  by  the  influence  of  A's  charge. 
This  phenomenon  may  be  called  "induction"  but,  as  will  be  seen 
later,  there  is  a  more  important  and  different  kind  of  induction 
and  it  is  better  to  use  the  term  "influence"  If  A  be  withdrawn, 
the  charge  upon  B  disappears. 

29.  Distribution  of  the  Induced  Charge. — If  we  return  to  the 
preceding  experiment  and  examine  B  while  it  is  under  the  in- 


18  ELEMENTS  OF  ELECTRICITY. 

fluence  of  A,  it  will  be  noticed  that  the  pairs  of  pith  balls  do  not 
diverge  to  the  same  extent,  those  at  the  ends  standing  far  apart 
but  the  divergence  decreasing  towards  the  center  and  the  pair  at 
the  center  not  diverging  at  all.  This  indicates  that  the  charge 
has  accumulated  at  the  ends  of  B  and  that  the  center  is  not  charged. 
Examination  with  an  electroscope  will  show  that  the  charges  at 
the  ends  of  B  are  of  different  kinds,  that  nearest  A  (in  the  case 
assumed)  being  negative,  that  farthest  away  being  positive;  in 
other  words,  the  positive  charge  on  A  has  induced  on  B  and  drawn 
as  near  to  itself  as  possible  a  negative  charge  and  repelled  as  far 
as  possible  a  positive  charge. 

In  Par.  24  it  is  stated  that  bodies  charged  with  like  electricity 
repel  each  other  and  those  charged  with  unlike  attract.  The 
above  experiment  seems  to  indicate  that  it  is  not  the  charged 
bodies  that  attract  or  repel  each  other  but  the  charges  them- 
selves; however,  as  we  can  not  obtain  a  charge  separate  from  a 
material  body  the  matter  is  not  susceptible  of  absolutely  convinc- 
ing proof. 

30.  Electric  Attraction  and  Repulsion  Explained. — The  fore- 
going affords  an  explanation  of  the  phenomena  of  attraction  and 
repulsion  already  described.    When  an  electrified  rod  is  presented 
to  a  pith  ball,  a  like  charge  is  induced  on  the  far  side  of  the  ball 
and  an  opposite  charge  on  the  near  side.     The  like  charge  is 
repelled,  the  opposite  attracted  and  the  opposite  being  the  nearer, 
the  force  of  attraction  is  greater  than  that  of  repulsion  and  the 
ball  moves  bodily  to   the  rod.     Upon   contact   with   the  rod 
the  opposite  charge  on  the  ball  is  neutralized  by  a  portion  of 
the  charge  on  the  rod,  leaving  the  ball  with  the  same  kind  of 
charge  as  that  remaining  on  the  rod  and  consequently  the  ball  is 
repelled. 

31.  Amount  of  Induced  Charge. — A  given  charge  always  in- 
duces on  surrounding  objects  an  exactly  equal  opposite  charge. 
If  a  small  charged  sphere  be  placed  at  the  center  of  a  hollow  con- 
ducting sphere  there  will  be  induced  upon  the  inner  surface  of  the 
latter  an  exactly  equal  opposite  charge,   and    this  no  matter 
what  the  size  of  the  outer  sphere  or  the  thickness  or  the  nature 
of  the  intervening  non-conductor.    If  the  charged  sphere  be  dis- 
placed from  the  center  so  as  to  be  nearer  one  side  of  the  cavity 
than  the  other,  the  amount  of  the  induced  charge  is  unaltered 


STATIC  ELECTRICITY.  19 

but  the  greater  portion  will  accumulate  upon  the  side  of  the 
cavity  nearest  the  sphere.  A  charged  body  inside  of  a  room 
induces  upon  the  ceiling,  walls,  floor  and  surrounding  objects 
opposite  charges  which  in  the  aggregate  exactly  equal  the  central 
charge  and  which  accumulate  most  upon  those  objects  nearest 
to  it.  Finally,  if  the  charged  body  be  at  a  distance  from  others, 
as  for  example  in  an  open  field,  the  induced  charge  will  still  be  the 
same  but  will  be  spread  over  the  surface  of  the  ground,  the  greater 
portion  being  immediately  beneath  the  body.  If  while  in  this 
position  a  conducting  body  be  brought  up  close  to  it,  practically 
the  entire  induced  charge  will  be  found  upon  the  second  body  and 
the  portion  upon  the  earth  becomes  so  small  that  it  may  be 
neglected.  In  ordinary  laboratory  experiments  where  the  charged 
body  is  a  foot  or  more  from  the  table  beneath  and  is  supported 
by  an  insulated  stem  and  the  conductor  upon  which  the  charge  is 
induced  is  brought  up  to  a  distance  of  an  inch  or  so  from  the  first, 
the  induced  charge  upon  the  table  and  more  distant  objects 
becomes  less  and  less  and  gathers  more  and  more  upon  the  con- 
ductor. Under  such  conditions  we  may  say  that  the  amount  of 
the  induced  charge  upon  the  conductor  depends  upon — 

(a)  The  amount  of  the  primary  or  inducing  charge; 

(b)  The  distance  between  the  primary  and  the  induced  charge; 

(c)  The  nature  of  the  medium  between  them. 

The  greater  the  primary  charge,  the  greater  its  influence  and  the 
greater  the  induced  charge. 

The  nearer  the  primary  charge  to  the  conductor,  the  greater 
the  induced  charge. 

With  a  constant  primary  charge  at  a  constant  distance  from  the 
conductor,  the  amount  of  the  induced  charge  is  found  to  vary  with 
the  nature  of  the  separating  medium,  that  is,  whether  it  be  air  or 
oil  or  glass  or  sulphur  or  mica  or  other  non-conductor  and  this 
variation  is  not  in  proportion  to  the  value  of  the  substance  as  a 
non-conductor  but  to  an  inherent  property  of  the  substance 
termed  by  Faraday  its  dielectric  capacity  (see  Par.  90). 

The  maximum  charge  that  could  ever  be  induced  is  one  at  the 
far  end  of  the  conductor  equal  and  similar  to  the  primary  charge 
and  one  at  the  near  end  equal  and  opposite.  As  the  distance 
between  the  primary  and  the  opposite  induced  charge  diminishes 
a  point  is  reached  where  the  attraction  between  them  becomes 


20 


ELEMENTS  OF  ELECTRICITY. 


great  enough  to  break  down  the  resistance  of  the  remaining 
thickness  of  the  medium  intervening,  a  spark  leaps  across,  the 
primary  charge  and  the  opposite  induced  charge  neutralize  each 
other,  the  original  charged  body  is  found  to  be  discharged  and 
the  conductor  is  left  charged  with  the  similar  charge  which  at 
first  was  repelled  to  its  far  end. 

32.  Separation  of  the  Induced  Charges. — If  we  repeat  the  pre- 
ceding experiment  with  the  charged  ball  A  and  a  divided  con- 


c 


B 


w 


ductor  consisting  of  two  parts  B  and  C,  Fig.  8,  which  may  be 
placed  in  close  contact,  the  induced  positive  charge  will  be  repelled 
Into  the  far  end  C  and  the  negative  charge  drawn  into  the  near 
end  B.  While  under  the  influence  of  A,  C  may  be  removed  first 
and  then  B  and  each  will  be  found  to  be  charged,  C  positively  and 
B  negatively.  If  the  two  parts  while  distant  from  A  be  again 
,  joined  together  their  electrifica- 

•"    tion  vanishes.    This  is  an  addi- 


c 


B 


~"\  tional  proof  of  the  fact  stated 

/  in  Par.  26  of  the  simultaneous 

production  of  equal  amounts  of 
both  kinds  of  electricity. 

33.  Free  and  Bound  Charges. 

—Let  us  again  consider  the  case 
of  the  charged  insulated  ball  and 
the  insulated  conductor  as  shown 
in  Fig.  9.  The  positive  charge  on 
A  has  induced  and  attracted  to  the  near  end  of  B  a  negative 
charge  which  is  held  securely  by  their  mutual  attraction.  The 
hand  may  be  placed  on  B,  a  wire  may  be  attached  to  the  near 


Fig.  9. 


STATIC  ELECTRICITY.  21 

end  of  Bf  still  the  negative  charge  refuses  to  budge  and  the  only 
way  by  which  it  can  be  made  to  shift  its  position  is  by  connect- 
ing it  to  some  conductor  which  will  allow  it  to  approach  A  nearer 
than  it  is  now.  Such  a  charge,  that  is  an  induced  charge  held  by 
a  primary  charge  of  the  opposite  kind,  is  said  to  be  "bound." 
On  the  other  hand,  the  positive  charge  on  the  far  end  of  B  is 
being  repelled  by  A  and  will  take  advantage  of  any  path  what- 
soever which  will  enable  it  to  withdraw  more  remote  from  A. 
Thus  if  the  hand  be  placed  upon  the  near  end  or  upon  any  other 
point  of  B  the  positive  cliarge  immediately  escapes  through  the 
body  and  finally  to  the  earth,  even  though  in  doing  so  it  must 
in  a  part  of  its  pathway  draw  nearer  to  A.  Such  a  charge,  in 
contradistinction  to  the  bound  charge,  is  said  to  be  "free"  and 
this  name  is  also  applied  to  any  charge  upon  an  insulated  con- 
ductor not  under  the  influence  of  some  other  charge.  Since  the 
free  charge  always  escapes  when  the  conductor  is  touched  and  the 
bound  charge  remains,  the  following  rule  is  given :  //  while  under 
the  influence  of  a  charged  body  a  conductor  be  touched,  it  acquires  a 
charge  of  the  opposite  sign. 

We  are  now  in  a  position  to  understand  the  operation  of 
two  pieces  of  apparatus,  the  gold-leaf  electroscope  and  the 
electrophorus. 

34.  The  Gold-Leaf  Electroscope. — This  is  a  very  sensitive  piece 
of  apparatus  for  detecting  the  presence  of  electric  charges  and 
determining  their  character.  The  simplest  form  consists  of  a 
glass  jar  (Fig.  10)  closed  by  a  stopper  of  insulating  material 
through  which  passes  a  brass  rod  which  terminates  above  in  a 
metal  knob  or  disc  and  below  is  bent  like  the  letter  L.  Fastened  to 
the  horizontal  arm  of  the  L  so  as  to  hang  face  to  face  in  contact 
and  vertically  are  two  small  ribbon-like  strips  of  gold-leaf.  This 
is  used  because  on  account  of  its  extreme  thinness  it  is  lighter  than 
any  other  material  of  equal  strength  and  adds  the  advantage  of 
being  an  excellent  conductor.  The  glass  jar  serves  as  an  insulating 
support  and  protects  the  leaves  from  currents  of  air  which  would 
cause  them  to  flutter.  When  a  charged  body,  such  as  an  electri- 
fied rod  of  glass  or  of  sealing  wax,  even  though  the  charge  be  very 
small,  is  brought  within  a  foot  or  so  of  the  apparatus  the  hanging 
leaves  will  diverge.  The  explanation  is  that  the  charged  body 
induces  and  attracts  an  unlike  charge  into  the  knob  of  the  appara- 
tus and  repels  a  charge  of  similar  kind  to  its  own  as  far  as  possible, 


22 


ELEMENTS  OF  ELECTRICITY. 


that  is,  into  the  gold  leaves;  these  having  like  charges  repel  each 
other  and  stand  apart. 

To  determine  the  nature  of  a  charge,  the  electroscope  is  given  a 
preliminary  charge  of  a  known  kind.    This  causes  the  leaves  to 


Fig.  10. 


diverge.  If  now  it  be  approached  by  a  charge  of  the  same  kind 
the  leaves  will  diverge  more  while  if  the  charge  be  of  opposite 
kind  they  will  droop  together. 

By  taking  advantage  of  the  principle  given  in  the  preceding 
paragraph  we  may  with  a  single  charged  body  impart  to  the 
electroscope  a  charge  of  either  kind  desired.  Thus  with  a  posi- 
tively charged  glass  rod  we  may  touch  the  knob  and  impart  a 
slight  positive  charge  (we  really  neutralize  the  induced  negative 
charge  in  the  knob  and  leave  the  induced  positive  charge).  To 
charge  it  negatively  we  hold  the  glass  rod  near  the  knob  (Fig.  10). 
This  induces  a  bound  negative  charge  and  a  free  positive  charge. 
If  now  the  knob  be  touched  by  the  remaining  hand  the  free  charge 
will  be  removed  as  will  be  indicated  by  the  leaves  instantly  falling 
together.  Now  withdraw  the  hand  and  finally  remove  the  rod. 
The  bound  negative  charge,  which  had  been  attracted  into  the 
knob,  will  surge  back  and  distribute  itself  as  will  be  shown  by  the 
leaves  again  diverging. 


STATIC  ELECTRICITY. 


23 


35.  The  Electrophorus. — Volta's  invention,  the  electrophorus, 
Fig.  11,  an  instrument  for  producing  static  charges  by  influence, 
consists  of  two  parts.  The  first, 
analogous  to  the  charged  rod  used  in 
the  experiments  described  in  the  pre- 
ceding paragraph,  is  a  flat  cake  of 
some  resinoid  body,  resin,  sealing 
wax,  sulphur,  vulcanized  rubber  or 
celluloid,  mounted  in  a  shallow 
metal  dish.  The  second^is  a  circu- 
lar disc  of  metal,  or  of  wood  covered 
with  tin-foil,  at  the  back  of  which  is  a 
glass  handle.  To  use  the  instrument, 
the  cake  dry  and  free  from  dust  is 
rubbed  with  a  warm,  dry,  woolen 

cloth  or  piece  of  fur.  It  thus  acquires  a  negative  charge.  The 
metal  disc  is  then  placed  upon  the  cake.  It  is  in  mathematical 
contact  with  the  cake  in  only  a  few  points  and  the  cake  being  a 
non-conductor  only  the  minute  portions  of  the  charge  at  these 
points  of  contact  flow  into  the  disc.  Therefore  the  disc  is  a  con- 
ductor separated  from  a  charged  body,  the  cake,  by  a  layer  of  air 
as  thin  as  a  sheet  of  paper  and  consequently  a  bound  positive 
charge  is  induced  upon  its  lower  face  and  a  free  negative  charge 
upon  its  upper  face.  While  in  this  condition  it  is  touched  by  the 
finger,  the  free  charge  escapes  and,  in  accordance  with  the  rule  in 
Par.  33,  it  is  left  with  a  positive  charge.  It  may  then  be  lifted  by 
the  glass  handle  and  its  charge  being  no  longer  bound  can  be  used 
to  give  a  spark,  to  charge  other  bodies,  etc.  As  practically  none  of 
the  primary  charge  on  the  cake  is  removed,  this  process  could  be 
repeated  an  indefinite  number  of  times  without  the  necessity  of 
recharging  the  cake  but,  as  a  matter  of  fact,  the  primary  charge 
gradually  weakens  due  to  leakage  into  the  air. 

In  the  production  of  electricity,  energy  must  always  be  expended. 
It  requires  more  force  to  pull  the  disc  away  from  the  charged  cake 
than  it  does  from  the  cake  before  it  is  charged;  the  extra  energy 
thus  expended  accounts  for  the  production  of  the  charge. 

Machines  have  been  invented  by  which  this  operation  of  bring- 
ing up  the  conductor,  touching  it  and  then  withdrawing  it  is  per- 
formed automatically  and  the  movement  of  these  machines,  being 
one  of  rotation,  the  production  of  the  charge  is  almost  continuous. 


24  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  5. 
DISTRIBUTION   OF   CHARGE. 

36.  Charge  on  a  Non-Conductor. — An  electric  charge  imparted 
to  a  body  is  differently  distributed  according  to  whether  the  body 
is  a  conductor  or  a  non-conductor.    In  the  case  of  a  non-conductor 
the  charge  clings  to  the  spot  where  it  was  generated  or  placed.    If 
a  stick  of  sealing  wax  be  rubbed,  only  the  part  which  has  been 
rubbed  will  be  found  to  be  charged.    If  a  cake  of  non-conducting 
material  be  touched  by  a  charged  body,  only  the  spots  actually 
touched  will  be  charged.    If  such  a  cake  be  charged  over  its  entire 
surface  and  then  be  touched  by  the  finger  or  by  a  conductor,  only 
the   spots  actually   touched   will   be   discharged.     Lichtenberg 
devised  a  means  by  which  the  above  may  be  shown  to  the  eye.    A 
charged  body  is  moved  like  a  pencil  over  a  dry  sheet  of  glass  or  of 
resin  and  a  pattern  is  traced.     Finely  powdered  red  lead  and 
sulphur  mixed  together  are  then  sifted  over  this  pattern  through 
a  piece  of  muslin.    In  the  mixing  and  sifting  the  red  lead  becomes 
positively  electrified,  the  sulphur  negatively,  and  if  the  original 
charge  be  positive,  the  sulphur  will  be  attracted,  the  red  lead 
repelled  and  there  will  be  produced  a  yellow  pattern  on  a  red 
back  ground.    In  performing  this  experiment  it  will  be  noticed 
that  the  sulphur  does  not  follow  absolutely  the  mathematical 
lines  originally  traced  but  spreads  slightly  in  mossy  or  frost-like 
patterns.     Charges  while  not  flowing  over  a  non-conductor  still 
have  a  tendency  to  creep  or  spread  and  the  fern-like  forms  are  due 
to  minute  particles  of  dust  which  lead  the  charge  now  in  one 
direction,  now  in  another. 

37.  Charge  on  a  Conductor. — On  the  other  hand,  a  charge 
imparted  to  any  point  of  a  conductor  spreads  immediately  over 
the  entire  body  and  if  a  charged  conductor  be  touched  at  any  point 
so  as  to  afford  a  path  to  the  earth  it  is  immediately  discharged. 
It  is  possible  with  the  apparatus  described  in  the  next  paragraph 
to  remove  a  portion  of  the  charge.    As  soon  as  this  portion  is 
removed  the  remaining  charge  redistributes  itself. 


STATIC  ELECTRICITY. 


25 


38.  The  Charge  Confined  to  the  Surface. — With  size,  shape  and 
other  conditions  constant  it  is  found  that  the  same  charge  may  be 
imparted  to  a  conductor  whether  it  be  solid 

or  hollow  or  even  made  of  non-conducting 
material  covered  with  tin-foil  or  gilded.  The 
inevitable  conclusion  is  that  the  charge 
resides  upon  the  surface  of  a  conductor.  This 
is  shown  directly  by  the  following  experi- 
ments. A  hollow  metallic  sphere  (Fig.  12) 
with  an  opening  in  its  top  and  mounted  upon 
a  glass  support  is  given  a  charge.  In  order  to 
take  a  sample  portion  of  a  charge  for  in- 
vestigation, Coulomb  devised  a  piece  of  ap- 
paratus which  he  called  a  proof  plane.  This 
is  a  little  circular  disc  of  metal  or  gilded  paper 
fastened  to  the  end  of  a  small  glass  rod.  If  the  disc  be  touched  to 
a  charged  body  it  receives  a  portion  of  the  charge  and  may  then 
be  removed,  and  the  charge  tested  by  an  electroscope  or  otherwise. 
If  the  charged  sphere  be  touched  by  a  proof  plane  it  will  part  with 
a  portion  of  its  charge.  If,  however,  the  proof  plane  be  inserted 
through  the  opening  in  the  sphere  and  the  inside  of  the  sphere  be 
touched,  the  plane  will  show  no  sign  of  any  charge. 

The  above  fact  may  be  even  more  conclusively  shown  as  follows : 
A  small  metal  ball  suspended  by  a  silk  thread  is  brought  into  con- 
tact with  the  outside  of  the  charged  hollow  sphere.  While  touch- 
ing the  sphere  it  is  practically  a  portion  of  the  latter's  outer  sur- 
face and  it  receives  a  charge.  The  charged  ball  is  then  lowered 
through  the  opening  until  it  touches  the  inside  of  the  sphere. 
At  that  instant  when  it  forms  a  part  of  the  latter's  inner  sur- 
face it  is  discharged,  the  charge  passing  through  to  the  outside  of 
the  sphere. 

Faraday  showed  the  same  thing  with  a  cylinder  of  wire  gauze 
instead  of  the  sphere. 

39.  Blot's  Experiment.— -Another  demonstration  of  the  surface 
distribution  of  the  charge  is  given  by  Biot's  experiment.    In  Fig. 
13,  A  is  an  insulated  metallic  sphere  and  B  and  C  are  glass-handled 
metallic  hemispheres  slightly  larger  than  the  sphere.    If  the  sphere 
be  charged  and  then  the  hemispheres  placed  so  as  to  completely 
cover  it  but  not  to  touch  it  the  charge  will  still  remain  on  the  sphere. 
If  the  covers  be  allowed  to  touch  the  sphere  the  charge  will  im- 


26 


ELEMENTS  OF  ELECTRICITY. 


mediately  pass  to  the  hemispheres  which  when  separated  will  be 
found  to  be  charged  and  the  sphere  discharged.  The  reason  for 
this  is  given  later  (Par.  68). 


c 


B 


Fig.  13. 

As  an  exception  to  the  foregoing  general  statement  there  is  one 
set  of  conditions  under  which  it  is  possible  to  have  a  charge  on  the 
interior  of  a  conductor.  If  through  the  opening  of  the  sphere 
shown  in  Fig.  12  there  be  inserted  a  charged  insulated  body,  there 
will  be  induced  upon  the  inside  of  the  surrounding  sphere  a  charge 
of  opposite  kind,  the  charge  of  like  kind  being  repelled  to  the 
exterior. 

Finally,  it  must  be  remembered  that  we  are  now  discussing 
static  charges,  for,  as  will  be  shown  later,  current  electricity 
penetrates  throughout  the  conductor. 

40.  Distribution  of  Charge. — Although,  as  was  stated  in  Par. 
37  above,  a  charge  imparted  to  a  conductor  spreads  over  it  im- 
mediately, the  distribution  is  not  uniform  but  more  of  the  charge 


a 


b  c 

Fig.  14. 

will  be  found  about  the  edges  and  angles  than  upon  the  flatter 
surfaces.  In  fact,  there  is  only  one  body,  the  sphere,  upon  which 
the  distribution  is  uniform  and  this  is  so  only  when  the  sphere  is 
so  remote  from  other  charged  bodies  that  the  effects  of  induction 


STATIC  ELECTRICITY.  27 

are  not  felt.  This  uniform  distribution  may  be  represented 
graphically  as  in  (a)  in  Fig.  14  by  drawing  about  the  circle  repre- 
senting the  sphere  a  concentric  dotted  circle  as  if  the  charge  were 
a  material  of  the  thickness  represented  by  the  distance  between 
the  full  and  the  dotted  circles. 

On  a  metallic  disc  (b)  the  charge  is  heaped  up  around  the  edges 
but  uniformly  distributed  over  the  flat  surfaces.  Advantage  is 
taken  of  this  in  a  piece  of  apparatus,  the  attracted  disc  electrom- 
eter (Par.  101). 

If  the  conductor  be  a  cylinder  with  rounded  ends  (c),  such  as 
is  used  with  many  electrical  machines,  the  amount  of  charge  at 
the  ends  is  much  greater  than  upon  the  cylindrical  portion. 

41.  Surface  Density. — This  material  conception  of  the  charge 
is  not  confined  to  graphic  representation  but  in  o*ur  calculations 
we  may  and  do  treat  it  as  if  it  were  a  substance  the  component 
particles  of  which  repel  each  other  and  combine  in  a  resultant 
action  upon  other  charges.    Thus  we  speak  of  it  as  spread  with  a 
certain  density  over  the  surface  of  a  conductor  or  as  being  denser 
at  certain  points  than  at  others.    This  surface  density  is  meas- 
ured by  the  amount  of  electrification  or  number  of  units  of  elec- 
tricity per  unit  area.    What  these  units  are  is  explained  later  (Par. 
56).    An  isolated  sphere  is  the  only  body  over  which  the  dis- 
tribution is  uniform  and  the  surface  density  is  determined  by 
dividing  the  total  charge  by  the  area  of  the  sphere. 

On  neither  conductors  nor  on  non-conductors  may  a  charge  be 
accumulated  indefinitely,  but  when  in  air  the  surface  density  at 
any  point  reaches  about  20  units  per  square  centimeter  a  discharge 
will  occur  either  along  the  surface  of  the  body  or  through  the  body 
or  through  the  surrounding  medium. 

42.  Effect  of  Points.— Coulomb  found  that  in  an  ellipsoid  of 
revolution  the  surface  density  at  the  extremities  of  the  axes  were 
to  each  other  as  the  lengths  of  the  respective  axes.    In  a  spindle- 
shaped  ellipsoid  where  the  axis  of  revolution  is  much  longer  than 
the  minor  axis  the  density  at  the  pointed  end  is  very  much  greater 
than  that  on  the  equatorial  surface,  and  this  disproportion  in- 
creases as  the  ellipsoid  becomes  more  and  more  pointed  until 
finally  the  particles  of  air  adjacent  to  the  point  become  charged. 
Having  like  charges,  these  particles  repel  each  other  and  are 
repelled  from  the  point.    They  therefore  move  off,  giving  way  for 


28 


ELEMENTS  OF  ELECTRICITY. 


others  which  likewise  become  charged  and  move  off,  thus  produc- 
ing a  continuous  electric  wind  and  rapidly  discharging  the  body. 
In  consequence  of  the  foregoing,  all  points,  sharp  corners  and 
angles,  unless  they  be  designedly  used,  are  carefully  avoided  in 
electrical  apparatus. 

43.  Franklin's  Experiment. — To  illustrate  the  effect  of  points 
Franklin  devised  the  following  experiment.  From  the  ceiling 
there  is  suspended  by  a  silk  thread  a  pith  ball  as  large  as  a  marble 
and  upon  the  floor  immediately  beneath  is  placed  a  glass  jar  upon 
whose  mouth  is  balanced  a  metal  ball  (Fig.  15).  The  thread  is  of 


Fig.  15. 

such  length  that  the  pith  ball  hangs  against  the  side  of  the  metal 
ball.  A  charge  is  communicated  to  the  metal  ball  and  the  pith 
ball  is  at  once  repelled  and  hangs  at  a  distance  of  four  or  five 
inches.  If  now  a  sharp-pointed  wire  or  a  needle  held  in  the  hand 
be  brought  up  to  within  six  or  eight  inches  of  the  metal  ball,  its 
charge  is  instantly  lost  as  will  be  shown  by  the  pith  ball  falling 
against  it  at  once.  In  the  dark  a  faint  light,  like  that  of  a  firefly, 
will  be  seen  around  the  point  of  the  needle.  Franklin  stated  that 
the  needle  drew  the  electric  fire  from  the  ball.  A  more  accurate 
explanation  is  that  the  charge  upon  the  ball  induced  up  through 
the  body  of  the  experimenter  and  out  to  the  needle  an  opposite 
charge  which  escaped  from  the  point,  passed  over  to  the  ball  and 
neutralized  its  charge.  This  experiment  is  noteworthy  as  it 
suggested  to  Franklin  the  invention  of  the  lightning-rod. 

44.  Other   Experiments   with   Points. — The  existence   of   the 
electric  wind  referred  to  above  can  be  shown  in  several  ways.    If 


STATIC  ELECTRICITY.  29 

a  point  attached  to  a  charged  conductor  be  held  near  the  face  the 
wind  can  be  distinctly  felt.  If  such  a  point  be  held  close  to  the 
flame  of  a  candle  the  flame  will  be  blown  to  one  side  or  perhaps 
even  extinguished. 

As  the  charged  particles  of  air  are  repelled  from  the  point,  the 
point  must  experience  an  equal 
repulsion  in  the  opposite  direction. 
This  is  illustrated  by  tjie  electric 
whirl  shown  in  Fig.  16.  It  consists 
of  a  light  metal  hub  with  a  set  of 
pointed  wire  spokes,  the  ends  all 
being  bent  at  right  angles  and  all 
pointing  in  the  same  direction, 
clockwise  or  counter-clockwise. 
The  hub  is  placed  upon  a  pointed  ^  77" 

pivot  so  as  to  turn  freely  like  a  com- 
pass needle.    The  pivot  is  connected  to  an  electric  machine  and 
when  a  continuous  charge  is  supplied  the  whirl  rotates  in  the 
opposite  direction  to  that  in  which  the  ends  of  the  wires  point. 

There  is  a  final  point  in  connection  with  this  electric  wind  which 
is  to  be  noted.  Just  as  the  spray  from  an  atomizer  moistens  the 
surface  against  which  it  is  directed,  so  the  electrified  particles  of 
air  striking  the  surface  of  a  non-conductor  impart  a  charge  to  this 
surface.  This  property  is  utilized  in  the  operation  of  certain 
electric  machines  described  in  the  next  chapter. 

45.  Division  of  Charge. — If  a  charged  body  be  brought  into 
contact  with  one  not  charged,  both  being  insulated,  the  charge  is 
divided  between  the  two  in  proportion  to  their  electric  capacities, 
a  property  to  be  defined  later  (Par.  79).  If  both  bodies  be  charged 
they  may  be  considered  to  make  common  stock  of  their  charges 
and  to  redistribute  the  total  as  stated  above.  This  is  true  as  well 
for  charges  of  opposite  kinds;  enough  of  the  greater  charge  is 
consumed  to  neutralize  the  lesser  and  the  remainder,  whether 
positive  or  negative,  is  distributed  between  the  two  bodies. 
Spheres  of  equal  size  have  equal  capacities,  therefore,  if  an  in- 
sulated charged  sphere  be  touched  by  an  equal  uncharged  one, 
likewise  insulated,  the  original  charge  will  be  divided  into  halves. 
This  enables  us  to  get  two  similar  and  equal  charges  and,  as  will 
shortly  be  shown,  is  of  very  great  importance  in  the  determina- 
tion of  the  laws  of  electrical  attraction  and  of  repulsion  and  in 
the  measurement  of  electrical  charges. 


30 


ELEMENTS  OF  ELECTRICITY. 


CHAPTER  6. 

ELECTRICAL   MACHINES. 

46.  Kinds  of  Machines. — In  the  preceding  chapters  we  have 
seen  how  electric  charges  may  be  produced  first  by  friction  of  dis- 
similar substances  and  second  by  influence,  as  typically  in  the 
case  of  the  electrophorus.    Based  upon  these  two  principles  there 
have  been  constructed  two  distinct  classes  of  machines  designated 
respectively  as  frictional  and  influence  machines.    These  substi- 
tute for  the  intermittent  motion  of  friction  and  for  the  alternate 
lowering  and  raising  of  the  disc  of  the  electrophorus  a  motion  of 
rotation  by  which  wasteful  expenditure  of  energy  is  avoided,  the 
production  of  the  charge  becomes  continuous,  and  a  much  greater 
charge  can  be  obtained  than  by  the  other  means.    Many  kinds 
have  been  constructed  and  though  they  are  of  interest  the  limits 
of  time  and  space  restrict  us  to  a  brief  description  and  explanation 
of  a  typical  form  of  each. 

47.  Frictional  Machines. — Frictional  machines  comprise  three 
parts,  the  material  which  is  rubbed,  the  rubber  and  the  body, 
called  the  prime  conductor,  upon  which  the  charge  is  accumulated. 


Fig.  17. 

The  earliest  form,  invented  by  Von  Guericke,  consisted  of  a  globe 
of  sulphur  cast  upon  a  wooden  axis  by  which  it  was  rotated.  As 
the  globe  revolved  it  was  pressed  by  the  bare  hand  and  the  charge 
was  gathered  by  a  light  chain  which  dangled  against  the  globe 


STATIC  ELECTRICITY.  31 

and  hung  from  the  prime  conductor,  an  iron  bar  suspended  by 
silk  chords.  Many  changes  and  improvements  were  made  by 
subsequent  inventors.  The  operation  of  the  modern  machine  is 
best  explained  from  the  form  shown  in  Fig.  17,  the  cylinder 
machine. 

48.  Cylinder  Machine. — This  consists  of  a  glass  cylinder  A 
rotating  on  a  horizontal  axis,  a  hair-stuffed  pad  B  pressing 
against  one  side  of  the  cylinder  and  the  prime  conductor  C  placed 
on  the  other  side  and  insulated  upon  a  glass  support.  This  con- 
ductor is  of  hollow  brass,  of  the  shape  shown,  from  one  end  of 
which  projects  a  T-shaped  rod  carrying  on  its  outer  side  a  row  of 
needle-like  spikes.  The  quantity  of  electricity  produced  depends 
upon  the  extent  of  the  two  surfaces  in  contact  and  also  upon  the 
material  of  which  these  consist.  The  farther  these  are  apart  in 
the  list  of  substances  in  Par.  23,  the  greater  the  electrical  effect 
produced  by  rubbing  them  together.  The  material  of  the  cylinder, 
glass,  being  near  the  top  of  the  list,  the  rubber  should  be  some 
substance  near  the  bottom.  The  metals  come  near  the  bottom 
but  their  rigidity  interferes  with  their  use  as  rubbers.  However, 
certain  metals  dissolve  readily  in  mercury  producing  a  more  or 
less  pasty  amalgam  which  alone  or  mixed  with  grease  may  be 
smeared  upon  the  rubber.  Zinc,  tin  and  the  sulphide  of  tin  are 
used  in  these  amalgams. 

The  operation  of  the  machine  is  as  follows:  The  cylinder  is 
rotated  in  a  clockwise  direction,  the  glass  becomes  positively 
electrified,  the  rubber  negatively.  As  the  positive  charge  on  the 
surface  of  the  glass  comes  around  opposite  the  prime  conductor, 
the  points  are  said  to  collect  it  or  take  it  off,  but  actually  a  nega- 
tive charge  is  induced  on  the  near  end  of  this  conductor,  a  positive 
charge  on  the  far  end,  the  negative  charge  escapes  from  the  needle 
points  in  an  electric  wind,  strikes  against  the  cylinder  and  neutral- 
izes the  positive  charge  on  its  surface  (Par.  43)  and  the  conductor 
acquires  an  increasing  positive  charge. 

If  the  rubber  is  insulated,  a  negative  charge  may  be  drawn  from 
it  but  it  is  generally  connected  to  the  ground  by  means  of  a  light 
chain  or  otherwise. 

More  modern  forms  use  rotating  glass  plates  instead  of  the 
cylinder  but  the  principle  of  their  operation  is  the  same.  It 
will  be  noted  that  although  designated  frictional  machines,  in- 
fluence as  well  as  friction  is  involved  in  the  production  of  the 


32 


ELEMENTS  OF  ELECTRICITY. 


charge.  '  They  are  very  sensitive  to  hygroscopic  moisture  and 
frequently  fail  to  work  on  account  of  atmospheric  conditions, 
for  which  reason  they  are  now  superseded  by  the  influence 
machines. 

49.  Toepler's  Influence  Machine. — This  machine,  as  shown  in 
its  simplest  form  in  Fig.  18,  consists  of  two  plates  of  glass  mounted 


Fig.  18. 

a  short  distance  apart  upon  a  common  horizontal  axis  about  which 
one  may  be  rotated,  the  other  one  being  fastened  rigidly  to  the 
frame  of  the  apparatus.  The  rotating  plate  is  circular  in  form. 
Fig.  19  (in  which  for  clearness  the  relative  proportions  and  posi- 
tions of  the  parts  have  been  greatly  distorted)  represents  an 
edgewise  view  of  the  glass  plates,  the  eye  of  the  observer  being 
supposed  to  travel  around  the  circumference  while  being  con- 
tinually directed  towards  the  axis  of  the  machine.  The  letters  on 
these  two  figures  correspond.  A  represents  the  fixed  plate  and  B 
the  moving  one,  the  direction  of  motion  being  indicated  by  the 
arrow.  On  the  outer  surface  of  A  and  diametrically  opposite  to 
each  other  are  the  two  field  plates  C  and  D.  These  are  sheets 
of  tin-foil  glued  to  the  glass,  their  thickness  being  greatly  exagger- 
ated in  Fig.  19.  Extending  from  each  of  these  field  plates  there  is 
a  conductor  which  passes  around  the  outer  edge  of  the  two  glass 
plates  to  the  appropriating  brushes  E  and  F  on  the  outer  side 


STATIC  ELECTRICITY. 


33 


of  the  revolving  plate.  These  brushes  are  of  fine  brass  wire 
like  a  paint  brush  and  sweep  along  the  face  of  the  plate  B  as 
it  revolves.  On  the  outer  surface  of  B  there  are  glued  six 
carriers,  G,  H,  J,  K,  L,  M, 
likewise  of  tin-foil.  Outside 
of  these  and  opposite  the 
farther  edge  of  the  field  plates 
are  the  neutralizing  brushes, 
N  and  P,  connected  to  each 
other  by  a  conductor.  Mid- 
way between  the  appropriating 
and  the  neutralizing  brushes 
are  the  two  combs,  Q  and  R, 
which  connect  to  the  two  dis- 
charging knobs,  S  and  T.  These 
knobs  are  on  the  ends  of  rods 
which  by  means  of  the  glass 
handles  U  and  W  may  be  slid 
in  or  out  thus  adjusting  the 
distance  between  the  knobs. 
The  operation  of  the  machine 
is  as  follows:  From  an  excited 
glass  rod  Z  a  small  initial 
charge  is  imparted  to  the  plate 
C.  This  induces  a  negative 
charge  on  the  inner  side  of  the 
carrier  H  and  a  positive  charge 
on  the  outer  side.  As  the  plate 
B  rotates  H  moves  to  the  po- 
sition J  where  it  is  touched 
by  the  neutralizing  brush  N 
which  allows  its  free  positive 
charge  to  escape,  as  shown  by  the  small  arrow,  and  leaves  it  with 
a  negative  charge.  Upon  reaching  the  position  K  the  greater 
part  of  this  negative  charge,  being  no  longer  bound,  is  drawn  off 
by  the  appropriating  brush  F  and  conveyed  to  the  field  plate  D. 
When  the  carrier  reaches  the  position  L  the  negative  charge  on  D 
induces  a  positive  charge  on  the  inner  surface  and  a  negative 
charge  on  the  outer.  In  the  position  M  the  carrier  is  touched  by 
the  neutralizing  brush  P  and  the  free  negative  charge  is  neutral- 


U 


34 


ELEMENTS  OF  ELECTRICITY. 


ized  by  the  positive  charge  coming  from  N,  M  being  left  with  a 
positive  charge.  The  carrier  next  reaches  G,  is  touched  by  the 
appropriating  brush  E  and  gives  up  the  greater  part  of  its  charge 
to  the  field  plate  C.  C  now  has  a  greater  positive  charge  than  in 
the  beginning  and  its  inductive  action  upon  H  is  greater.  In  this 
manner  as  the  carriers  rotate  they  add  to  the  charges  on  the  field 
plates.  This  does  not  continue  indefinitely.  The  field  plate  C 
being  much  larger  than  the  carrier  G  has  a  much  greater  capacity. 
This  property  is  defined  later  but  for  the  present  we  may  say  (in 
a  figurative  sense)  that  C  requires  more  electricity  to  fill  it  up 
than  does  G  but  once  that  it  is  filled  up  no  more  will  flow  into  it 
from  G.  However,  induction  continues  to  act  and  the  unappro- 
priated charges  on  the  carriers  are  now  taken  off  by  the  combs 
Q  and  R  as  was  explained  in  the  description  of  the  frictional 
machine,  and  it  is  this  surplus  electricity  which  we  draw  from  the 
machine.  In  this  machine,  as  in  the  frictional  machine,  it  will  be 
noted  that  two  kinds  of  electricity  are  involved  in  the  production 
of  the  charge,  the  initial  charge  being  produced  by  frictional 
electricity. 

50.  Holtz's  Influence  Machine. — In  construction  this  is  a  much 
simpler  machine  than  Toepler's.  It  consists  (Fig.  20)  of  two  cir- 
cular glass  plates  face  to  face,  one  fixed,  the  other  rotating,  two 
field  plates  and  two  combs  with  adjustable  discharging  knobs. 

At  the  opposite  extremities  of 
a  diameter  of  the  fixed  plate, 
window-like  openings  are  cut 
and  on  the  corresponding  side 
of  each  of  these  openings  are 
pasted  the  paper  field  plates. 
Fig.  21  represents  an  edgewise 
view  of  the  machine.  B  is  the 
rotating  plate,  the  direction  of 
its  motion  being  indicated  by 
the  arrow.  A  is  the  fixed 
plate  with  the  windows  and  C 
and  D  are  the  paper  field  plates.  Extending  from  the  field  plates 
over  the  edge  of  the  openings  are  either  tongue-like  strips  as 
shown  or  else  a  series  of  sharp  metal  points.  The  operation  of 
the  machine  in  detail  is  as  follows: 

The    discharging   knobs  G   and    H   are   placed    in    contact. 


Fig.  20. 


STATIC  ELECTRICITY. 


35 


The  field  plate  C  is  given  a  small  initial  charge,  say  positive. 
This  induces  a  negative  charge  on  F  and  repels  a  positive  charge 


B 


& 


toE. 

An  electric  wind  escapes  from  F  upon  B 
and,  as  explained  in  Par.  43,  charges  the  sur- 
face of  B  negatively. 

The  positive  charge  on  E  induces  a  nega- 
tive charge  in  D.  A  positive  electric  wind 
escapes  from  E  upon  B  and  neutralizes  the 
negative  charge  brought  along  the  surface 
from  F. 

A  positive  wind  escapes  from  the  point  of 
D  and  charges  the  inner  surface  of  B  posi- 
tively. As  this  positive  charge  approaches 
C  a  negative  wind  escapes  from  C  and  neu- 
tralizes it.  The  escape  of  this  negative 
electricity  from  C  leaves  C  more  highly 
charged  positively  and  C  exerts  more  induc- 
tion upon  F. 

This,  as  explained  above,  makes  D  more 
highly  charged  negatively  and  so  on,  the 
"building  up"  continuing  as  the  plate  B 
rotates. 

Finally,  when  the  discharging  knobs  are 
separated,  a  large  positive  charge  is  induced 
in  E  and  a  corresponding  negative  one  in 
its  knob  G,  while  a  large  negative  charge  is 
induced  in  F  and  a  corresponding  positive 
one  in  H  and  the  attraction  between  the 
two  in  G  and  H  is  sufficient  to  drive  sparks 
across  the  gap  between  the  knobs,  this  gap  being  much  shorter 
than  the  distance  between  C  and  D. 

Influence  machines  are  sensitive  to  atmospheric  moisture  but 
not  to  the  same  extent  as  the  frictional  machines,  one  reason  being 
that  the  glass  plates  of  the  influence  machines  may  be  coated  with 
varnish  which  in  a  measure  prevents  the  deposition  of  moisture 
while  in  the  frictional  machines  the  plates  must  be  kept  free. 

Those  influence  machines  which  employ  appropriating  brushes 
are  self-exciting,  that  is,  the  slight  friction  of  these  brushes  is 
enough  to  start  the  machine  in  operation  when  the  plate  is  re- 


D 


D 


B 
Fig.  21. 


36  ELEMENTS  OF  ELECTRICITY. 

volved,  but  the  machines  of  the  Holtz  type  must  be  given  an 
initial  charge. 

51.  Electrical  Diagrams.— The  illustrations  (Figs.  19  and  21) 
in  the  preceding  paragraphs  are  examples  of  a  class  of  figures 
termed  diagrammatic  which  are  largely  used  in  the  study  of 
electricity.  In  these  the  main  object  is  to  bring  out  clearly  the 
essential  arrangements,  connections  and  principles  and  to  this  end, 
when  necessary,  details  are  omitted,  the  rules  of  perspective  are 
ignored,  proportions  are  distorted  and  relative  positions  changed. 
Conventional  signs  are  frequently  used,  a  simple  character  stand- 
ing for  a  piece  of  apparatus  like  a  cell  or  for  a  complicated  machine 
like  a  dynamo.  Many  examples  will  be  noticed  in  the  following 
pages. 


STATIC  ELECTRICITY. 


37 


CHAPTER  7. 

LAWS   OF   ELECTRIC   ATTRACTION 
AND   REPULSION. 

52.  Coulomb's  Torsion  Balance. — At  various  points  in  the 
preceding  pages  it  has  been  shown  that  charges  differ  from  one 
another  in  quantity  and  that  the  force  of  electric  attraction  and  of 
repulsion  varies  both  with  the  quantity  of  the  charges  and  with 
the  distance  between  the  charged  bodies.  In  the  present  chapter 


F-- 


Fig.  22. 


we  shall  see  what  are  the  laws  governing  this  attraction  and  repul- 
sion and  also  how  and  by  what  units  charges  may  be  measured. 
The  first  exact  experimental  determinations  of  the  laws  of 
electrical  attraction  and  repulsion  were  made  by  Coulomb  with 


38  ELEMENTS  OF  ELECTRICITY. 

an  instrument  called  by  him  the  torsion  balance.  This  is  shown  in 
Fig.  22  and  consists  of  a  vertical  glass  cylinder  B  graduated  in 
degrees  around  a  belt  a  little  below  its  middle  and  covered  with  a 
top  which  is  pierced  with  two  circular  openings,  one  in  the  center 
and  a  smaller  one  near  the  edge.  Around  the  central  opening 
stands  a  second  and  smaller  vertical  glass  cylinder  C  (represented 
in  the  figure  as  being  partly  cut  away).  This  smaller  cylinder 
carries  on  its  top  a  metal  cap  D  graduated  around  its  edge  in 
degrees  and  pierced  in  its  center  with  a  small  hole  in  which  fits 
a  metal  spindle  which  may  be  turned  by  means  of  the  milled  head 
E.  Projecting  from  the  shoulder  below  the  milled  head  is  the 
pointer  F  which  travels  over  the  graduated  edge  of  the  cap  and 
thus  indicates  the  number  of  degrees  through  which  the  spindle 
has  been  turned.  Hanging  from  the  spindle  is  a  delicate  silver 
wire  to  the  lower  end  of  which  there  is  attached  so  as  to  swing  in 
the  plane  of  the  graduations  a  needle  of  shellac.  At  one  end  of 
this  there  is  a  gilded  pith  ball  G,  about  four-tenths  of  an  inch  in 
diameter,  and  at  the  other  end  a  sufficient  counterweight  to  hold 
the  needle  horizontal.  In  the  second  opening  in  the  cover  of  the 
larger  cylinder  there  fits  a  handled  stopper  K  from  which  extends 
downward  a  needle  of  shellac,  or  of  paraffine-coated  glass,  ter- 
minating in  a  second  gilded  pith  ball  H  of  the  exact  size  of  the 
first.  The  centers  of  the  two  balls  lie  in  the  same  horizontal  plane. 
Finally,  the  instrument  stands  upon  a  bed  plate  A  furnished  with 
levelling  screws  by  means  of  which  the  silver  wire  can  be  brought 
to  coincide  with  the  axis  of  the  larger  cylinder. 

The  operation  of  the  instrument  is  as  follows:  It  is  first  care- 
fully levelled  and  then  the  milled  head  E  is  turned  until  the  ball 
G  is  just  tangent  to  the  ball  H.  In  this  position  the  plane  through 
the  suspending  silver  wire  and  the  center  of  the  ball  G  passes 
through  the  zero  of  the  graduated  scale  on  the  larger  cylinder.  K 
is  now  removed,  a  charge  is  imparted  to  H  and  K  is  then  rein- 
serted. As  H  touches  G  the  charge  on  H  is  distributed  between 
the  two  balls.  Having  similar  charges  H  and  G  repel  each  other 
and  G  (in  the  case  represented  in  the  figure)  swings  off  to  the  right 
and  as  it  does  so  twists  the  suspending  silver  wire.  Now  there  is 
a  definite  law  that  when  a  body  such  as  a  wire  is  twisted  by  a  force, 
its  elastic  limit  not  being  exceeded,  the  resistance  offered  to  the 
twisting,  or  the  tendency  to  untwist,  increases  directly  with  the 
angle  through  which  it  is  twisted  and  consequently  the  angle 


STATIC  ELECTRICITY.  39 

through  which  it  is  twisted  is  directly  proportional  to  the  force 
exerted.  The  force  which  will  twist  a  wire  through  ten  degrees  is 
exactly  double  that  which  will  twist  it  through  five  degrees.  As 
G  moves  to  the  right  the  resistance  of  the  wire  to  twisting  increases 
and  as  the  distance  between  G  and  H  increases  the  repelling  force 
grows  weaker  until  finally  a  position  of  equilibrium  is  reached, 
G  comes  to  rest,  and  the  angle  through  which  it  has  turned  can  be 
read  from  the  scale  on  the  surface  of  the  cylinder. 

53.  The  Law  of  Inverse  Squares. — By  means  of  the  torsion 
balance  Coulomb  demonstrated  that  electric  attraction  and  repul- 
sion followed  the  law  of  inverse  squares,  or  that  the  force  exerted 
between  two  charged  bodies  varies  inversely  as  the  square  of  the  dis- 
tance between  these  bodies.  Two  charged  bodies  which  at  a  certain 
distance  repel  each  other  with  a  certain  force  will  repel  each  other 
with  only  one-fourth  of  this  force  if  the  distance  be  doubled,  or 
one-ninth  if  it  be  trebled,  etc.  His  experiment  was  conducted  as 
follows:  The  balls  H  and  G  (Fig.  22)  were  charged  as  explained  in 
the  preceding  paragraph  and  let  us  suppose  that  the  movable  ball 
G  was  repelled  until  it  swung  through  an  angle  of  16  degrees.  By 
turning  the  milled  head  E  in  the  direction  shown  by  the  arrow  an 
additional  twist  was  put  upon  the  silver  wire  and  the  ball  G  was 
gradually  forced  back  towards  H.  When  G  had  thus  been  twisted 
back  to  within  8  degrees  of  H  it  was  found  that  the  pointer  F  of 
the  milled  head  had  travelled  over  56  degrees  of  the  scale  on  the 
cap  D.  The  total  angular  torsion  on  the  wire  was  consequently 
8+56  =  64  degrees.  The  force  exerted  in  the  two  cases  was,  there- 
fore, as  64  is  to  16,  which  is  the  same  as  four  to  one.  For  small 
angles  the  chords  bear  to  each  other  practically  the  same  ratio  as 
their  arcs,  hence  at  sixteen  degrees  the  balls  were  twice  as  far  apart 
as  at  eight  degrees,  or  as  the  distance  between  the  balls  was  divided 
by  two  the  force  between  them  was  multiplied  by  2x2  and  this 
conforms  to  the  law  of  inverse  squares.  These  results  are  con- 
firmed by  experiments  based  upon  other  methods. 

In  the  foregoing  illustration  the  figures  were  selected  to  fit  the 
demonstration  but  to  obtain  such  accurate  results  in  practice 
requires  very  careful  manipulation  and  the  observance  of  many 
precautions.  The  most  troublesome  source  of  error  is  loss  of  a 
portion  of  the  charge  during  the  progress  of  the  experiment.  The 
shellac  needles  to  which  the  balls  are  fastened  are  non-conductors 
when  free  from  hygroscopic  moisture  but  a  film  soon  deposits 


40  ELEMENTS  OF  ELECTRICITY. 

upon  them  from  the  air  and  leakage  of  charge  results.  To  remedy 
this  there  is  placed  in  the  instrument  a  small  saucer  containing 
quicklime  or  calcium  chloride  or  sulphuric  acid  which  substances 
have  a  great  affinity  for  water  and  thoroughly  dry  the  air  inside 
of  the  cylinder. 

A  similar  experimental  demonstration  can  be  made  in  the  case 
of  the  attraction  between  unlike  charges  but  the  manipulation 
is  much  more  difficult.  The  two  balls  must  separately  be  given 
charges  of  the  opposite  kind,  they  attract  each  other  and  a  con- 
dition of  unstable  equilibrium  exists.  Should  they  touch,  their 
charges  are  neutralized  and  the  process  must  be  rebegun. 

From  the  foregoing  it  will  be  seen  that  electric  attraction  and 
repulsion  follow  the  law  of  central  forces.  In  order  that  the  law 
of  inverse  squares  should  be  strictly  true,  the  charged  bodies  must 
be  small  spheres,  so  small  as  to  approximate  points,  and  should 
be  at  such  distance  apart  that  in  comparison  with  this  distance 
their  own  dimensions  are  negligible.  To  other  bodies  the  law 
does  not  apply.  The  force  between  two  charged  flat  discs  near 
together  does  not  vary  with  small  variations  in  the  distance. 

54.  Variation  of  Force  with  Charges. — The  force  exerted  between 
two  charged  bodies  varies  as  the  product  of  the  charges.     Reflection 
will  show  the  truth  of  this  second  law.     If  two  charged  bodies 
repel  or  attract  each  other  and  the  charge  of  either  one  be  doubled 
or  trebled,  the  repulsion  or  attraction  must  likewise  be  doubled  or 
trebled.     If  the  charge  of  the  second  one  be  now  doubled  or 
trebled,  the  existing  force  will  be  doubled  or  trebled,  that  is,  the 
original  force  will  be  multiplied  by  four  or  six  or  nine.    This  law 
may  be  demonstrated  by  the  torsion  balance.    It  will  be  remem- 
bered that  the  two  balls  G  and  H  (Fig.  22)  are  of  exactly  the  same 
size,  therefore,  no  matter  what  charge  we  start  with,  as  soon  as 
the  balls  have  touched  they  (in  accordance  with  the  principle 
stated  in  Par.  45)  divide  the  charge  equally  and  we  have  two 
similar  and  equal  charges.    We  may  determine  the  angular  repul- 
sion between  these,  then  withdraw  the  fixed  ball  H,  touch  it  to  a 
third  and  equal  ball  thereby  halving  its  charge,  return  H  to  the 
cylinder,  determine  the  new  angular  repulsion  and  hence  the 
variation  in  the  repulsion  with  the  variation  in  the  charge. 

55.  Variation  of  Force  with  Intervening  Medium. — Those  non- 
conducting substances  which  surround  charged  bodies  and  through 


STATIC  ELECTRICITY.  41 

which  electric  effects  are  transmitted  were  termed  by  Faraday 
"dielectrics."  The  force  of  attraction  or  of  repulsion  between 
charged  bodies  varies  with  the  nature  of  the  dielectric.  Thus  two 
small  similarly-charged  spheres  which  at  a  certain  distance  apart 
in  air  repel  each  other  with  a  force  of  so  many  dynes  will,  if  kept 
at  the  same  distance  and  immersed  in  oil,  repel  each  other  with  a 
force  only  one-half  as  great,  or,  if  separated  by  an  equal  thickness 
of  mica  will  repel  each  other  with  a  force  only  one-sixth  as  great. 
The  force  between  two  charged  bodies  in  air  is  not  varied  by  com- 
pressing or  by  rarifying  the  air  and  for  this  reason  and  on  account 
of  the  absence  of  any  absolute  measure  we  use  air  as  our  standard. 
The  ratio  of  the  force  exerted  between  two  charged  bodies  in  a 
certain  dielectric  to  the  force  exerted  between  the  same  bodies 
with  the  same  charges  at  the  same  distance  apart  in  air  may  be 
called  the  dielectric  coefficient  of  repulsion  and  is  the  coefficient 
by  which  the  force  exerted  between  two  charged  bodies  in  air 
would  be  multiplied  in  order  to  obtain  the  force  between  the  same 
two  bodies  under  the  same  conditions  in  the  medium  to  which  the 
coefficient  pertained.  For  oil  this  would  therefore  be  1/2,  for 
mica  1/6,  etc. 

For  gases  and  liquids  this  coefficient  might  be  determined  by 
the  use  of  Coulomb's  balance  as  explained  above  but  it  is  obvious 
that  this  method  could  not  be  applied  to  solids.  However,  we  shall 
see  later  on  (Par.  91)  how  it  may  be  otherwise  determined  and  at 
the  same  time  it  will  be  shown  why  it  is  written  in  the  form  of  a 
fraction  or  as  I/  k. 

In  problems  involving  forces  exerted  between  charged  bodies 
in  other  media  than  air,  the  appropriate  value  of  1/fc  should  be 
used  and  when  in  discussions  in  the  following  pages  this  coefficient 
does  not  appear  it  is  to  be  understood  that  the  dielectric  is  air. 

56.  Unit  Quantity  of  Electricity.  —  Representing  by  /  the  force 
of  attraction  or  of  repulsion,  by  q  and  q'  the  two  charges  and  by 
d  their  distance  apart  we  may  combine  the  three  laws  discussed 
above  and  express  them  mathematically  thus 


Since,  as  was  explained  in  Par.  10,  electricians  have  agreed  to 
follow  the  C.  G.  S.  system  of  units,  /  in  this  expression  must  be 
measured  in  dynes  and  d  in  centimeters.  In  the  torsion  balance 


42  ELEMENTS  OF  ELECTRICITY. 

where  the  two  gilded  pith  balls  were  of  equal  size,  q  and  q'  are 
equal,  and  since  the  dielectric  is  air,  l/k  =  1,  hence  the  above  ex- 
pression becomes 


If  we  assume  /  to  be  one  dyne  and  d  to  be  one  centimeter  we 
obtain  q  =  l,  whence  follows  at  once  the  definition:  An  electro- 
static unit  of  electricity  is  that  quantity  which  when  placed  at  a  centi- 
meter's distance  in  air  from  a  similar  and  equal  quantity  repels  it 
with  a  force  of  one  dyne. 

The  expression  "in  air"  is  essential  to  this  definition  as  is  also 
the  term  "electrostatic"  for,  as  we  shall  see  later  (Par.  228),  there 
is  another  and  different  unit  of  quantity,  the  coulomb,  which  is 
based  upon  current  relations.  The  coulomb  is  three  billion 
<3xl09)  times  as  large  as  the  electrostatic  unit. 


STATIC  ELECTRICITY.  43 


CHAPTER  8. 

ELECTRIC   FIELD. 

57.  Electric  Field. — We  have  seen  that  a  charged  body  attracts 
non-electrified  bodies  and  others  with  opposite  charge  and  repels 
those  with  similar  charge,  therefore,  in  the  space  around  an  elec- 
trified body  all  bodies  experience  a  force  either  of  attraction  or  of 
repulsion  and  this  space  is  called  the  field  of  the  charge.    As  we 
recede  from  the  charged  body  the  force  falls  off  rapidly  and  to  fix 
its  limits  with  more  definiteness  we  define  the  electric  field  as  that 
space  surrounding  a  charged  body  in  which  the  force  of  attraction  or 
of  repulsion  is  perceptible.    If  there  be  more  than  one  charged  body 
involved  each  produces  a  certain  effect  and  they  have  a  resultant 
field.    The  medium  within  the  limits  of  a  field  is  not  passive  or 
inert  but  takes  part  in  the  transmission  of  the  electrical  effects 
and  is  subjected  to  certain  mechanical  strains.     Between  two 
oppositely  charged  bodies  there  is  a  tension  as  if  they  were  being 
pulled  together  by  invisible  rubber  bands  and  at  the  same  time  a 
stress  at  right  angles  to  the  bands  pushing  the  bands  apart. 

58.  Intensity  of  Field. — It  may  aid  the  beginner  in  his  concep- 
tion if  he  consider  a  field  as  analogous  to  a  current  of  water.    In 
the  electric  field  there  is  no  matter  in  actual  movement  but  in  a 
sense  there  is  a  flow  of  force  and  -light  charged  bodies,  such  as  pith 
balls,  if  their  charges  are  all  of  one  kind,  will  be  swept  along  in  one 
direction  just  as  corks  are  carried  by  a  river.     In  order  that  a 
charged  body  be  acted  upon  it  must  be  in  the  field,  just  as  the  corks 
to  be  carried  along  must  be  in  the  stream.    Finally,  as  we  may 
measure  the  strength  of  a  stream  by  the  push  it  exerts  upon  a 
board  of  unit  area  inserted  in  it,  so  we  measure  the  strength  or 
intensity  of  a  field  by  the  push  it  exerts  upon  a  unit  charge  placed 
in  it.    We  therefore  define  a  unit  field  as  that  field  which  acts  with 
a  force  of  one  dyne  upon  a  unit  charge  placed  in  it.    It  follows  from 
the  deduction  of  Par.  56,  that  the  field  produced  at  a  distance  d 
in  air  from  a  charge  q  must  be  q/d2.    In  any  other  medium  than 
air  the  field  must  be  q/kd2.    If  we  say  that  a  field  has  a  strength  of 


44 


ELEMENTS  OF  ELECTRICITY. 


three  we  mean  that  it  will  pull  or  push  such  a  unit  charge  with  a 
force  of  three  dynes.  If  the  charge  itself  be  not  unity,  the  force 
with  which  it  is  acted  upon  is  equal  to  the  product  of  the  charge 
by  the  strength  of  the  field. 

59.  Direction  of  Field. — Suppose  that  we  have  a  horizontal  sheet 
of  glass  in  whose  center  there  is  a  charged  metal  sphere  (Fig.  23). 


Fig.  23. 

If  a  small  pith  ball  be  released  upon  the  glass  anywhere  near  the 
sphere,  it  will  first  be  attracted  to  the  sphere,  will  become  charged 
and  will  then  be  shot  away  in  a  radial  line.  The  force  acts  along 
these  lines  and  they  therefore  indicate  the  direction  of  the  field. 
Since  opposite  charges  would  move  in  opposite  directions  we,  by 
convention,  define  the  positive  direction  of  a  field  as  that  direction  in 
which  a  free  positive  charge  would  move. 

I 


Fig.  24. 

If  we  continue  this  experiment,  substituting  for  the  single  sphere 
two  placed  some  distance  apart  and  charged,  one  positively,  the 
other  negatively  (Fig.  24),  the  pith  ball  will  no  longer  follow 


STATIC  ELECTRICITY. 


45 


rectilinear  paths  but  curves  emerging  from  one  sphere  and  enter- 
ing the  other.  These  curves  indicate  the  direction  of  the  resultant 
field  at  the  successive  points  through  which  they  pass.  A  posi- 
tively-charged ball  at  C  is  repelled  by  A  along  the  line  CD  and 
attracted  by  B  along  the  line  CE.  A  being  the  nearer,  the  force 
CD  is  greater  than  CE  and  the  ball  moves  along  the  resultant  CF 
which  indicates  therefore  the  direction  of  the  field  at  the  point  C. 
The  space  about  the  two  spheres  may  be  regarded  as  permeated 
with  similar  lines  symmetrically  distributed  around  the  line  join- 
ing the  two  centers. 


Fig.  25. 

Had  the  two  spheres  contained  like  charges,  the  paths  would 
have  been  as  represented  in  Fig.  25. 

60.  Lines  of  Force. — These  lines  indicating  the  direction  of  the 
resultant  electric  force  at  the  points  in  the  field  through  which 
they  pass  are  called  lines  of  force.    They  start  from  a  positively- 
charged  surface  and  terminate  upon  a  negatively-charged  surface. 
They  therefore  have  opposite  charges  at  their  two  ends  and  never 
extend  between  bodies  with  like  charges.    They  never  penetrate 
below  the  surface  or  pass  through  a  conductor.    They  are  always 
perpendicular  to  the  terminal  surfaces  at  the  points  of  origin  and 
termination,  otherwise  there  would,  be  a  component  parallel  to 
the  surface  and  a  movement  of  electricity  along  this  surface  would 
result.    They  never  intersect,  for  in  that  case  two  tangents  could 
be  drawn  at  one  point,  that  is,  there  could  be  two  resultants  at 
one  point  which  is  an  absurdity.     It  follows  from  the  foregoing 
that  every  electric  field  consists  of  non-conductors  and  is  bounded 
by  conductors. 

61.  Graphic  Representation  of  Intensity  of  Field. — In  mechan- 
ics, in  order  to  treat  graphically,  to  discuss  mathematically  and 


46  ELEMENTS  OF  ELECTRICITY. 

to  interpret  geometrically  problems  involving  parallel  forces  dis- 
tributed over  a  surface  or  among  the  particles  of  a  mass  we,  by 
convention,  represent  the  direction  and  the  intensity  of  the  forces 
by  the  direction  and  length  respectively  of  a  right  line  and  for  the 
entire  system  may  substitute  a  single  resultant  whose  length  is 
the  sum  of  the  lengths  of  the  separate  components  and  whose 
point  of  application  is  the  center  of  gravity  of  the  surface  or  of 
the  mass.  In  the  case  of  electric  fields  however,  the  intensity 
varies  from  point  to  point  and  in  general  the  lines  of  force  are  not 
parallel,  therefore,  instead  of  representing  this  intensity  by  the 
length  of  a  resultant,  we  agree  to  represent  it  by  the  number 
of  lines  of  force  per  unit  of  area,  the  area  being  taken  perpen- 
dicular to  the  lines.  By  convention,  therefore,  a  unit  field  is  that 
field  which  contains  one  line  of  force  per  square  centimeter  of  cross- 
section. 

It  is  not  meant  by  this  convention  that  in  moving  about  in  a 
unit  field  the  force  is  experienced  at  intervals  of  one  centimeter 
only  and  that  the  intervening  space  is  blank,  any  more  than  by 
representing  the  attraction  of  gravity  upon  a  body  by  a  single  line 
we  imply  that  there  is  no  gravity  in  the  adjacent  space.  In  a 
similar  manner  we  might  consider  beams  of  light  as  made  up  of  a 
number  of  parallel  lines  or  rays  and  might  agree  to  measure  the 
intensity  of  the  beam  by  the  number  of  rays  per  centimeter  of 
cross-section.  Two  beams  of  light  passing  through  circles  of  the 
same  size  may  differ  in  intensity  and  therefore  include  a  different 
number  of  rays,  yet  on  a  cross-section  of  each  the  illumination  is 
uniformly  and  continuously  distributed,  so  two  fields  may  differ 
in  intensity  yet  in  each  the  force  exists  at  every  point. 

In  representing  lines  of  force  graphically  the  positive  direction, 
or  direction  in  which  a  free  positive  charge  would  move,  should 
always  be  indicated  by  arrow-heads. 

We  conclude  by  saying  that  lines  of  force  are  those  imaginary 
lines  in  a  field  which  by  their  direction  indicate  the  direction  of  the 
resultant  field  and  by  their  number  indicate  its  intensity. 

62.  Tubes  of  Force. — Another  convention  which  avoids  this 
apparent  intermittent  distribution  of  the  lines  of  force  and  which 
is  much  used  in  mathematical  discussions  of  electric  fields  is  that 
of  tubes  of  force.  There  are  supposed  to  originate  from  the  surface 
of  a  positively-charged  body  certain  tubular  surfaces  various  in 
cross-section  and  frequently  curved  but  lying  side  by  side  like  the 


STATIC  ELECTRICITY.  47 

cells  of  a  honeycomb  and  including  within  themselves  all  the 
space  about  the  body.  Their  walls  are  parallel  to  the  lines  of  force 
of  the  field  and  therefore  at  every  cross-section  of  one  of  these 
tubes  the  same  number  of  lines  would  be  cut.  They  terminate 
upon  a  negatively-charged  surface.  If  the  portion  of  the  surface 
of  the  charged  body  included  in  the  base  of  the  tube  contains  one 
unit  of  electricity,  the  tube  is  called  a  unit  tube.  It  follows  from 
this  conception  (and  also  from  Par.  31)  that  the  quantities  of 
electricity  upon  the  terminal  surfaces  of  a  tube  are  equal  and 
opposite  and  a  further  consequence  is  that  in  the  case  of  two 
parallel  planes  near  together,  one  of  which  is  charged,  the  tubes 
at  a  distance  from  the  edges  are  parallel  and  the  surface  density 
upon  the  central  portions  of  the  two  planes  equal  and  of  opposite 
signs.  This  principle  is  utilized  in  the  attracted  disc  electrometer 
described  later  (Par.  101). 

It  is  difficult  to  represent  these  tubes  graphically  and  we  gener- 
ally do  so  by  drawing  a  single  line  supposed  to  be  the  axis  of  the 
tube,  so  that  after  all  we  resort  to  lines  of  force. 

63.  Lines  of  Force  from  Unit  Charge.— If  in  Fig.  26  A  repre- 
sents a  unit  charge  and  B  a  similar  and  equal  charge  at  a  distance 

of  one  centimeter  from  A,  B  will  be  re-          ^~ ^ 

pelled  with  a  force  of  one  dyne.    A  unit     /'  ^^\ 

field  is  that  field  which  acts  with  a  force  of   /  \ 

one  dyne  upon  a  unit  charge  placed  in  it.  /  ^  \ 

A  is  surrounded  by  its  own  field  and  B  is  J  vx  (p  ^ 

in  it,  therefore  at  B  there  is  a  unit  field.  V%  / 

The  same  is  true  for  every  point  at  a  dis-    \  / 

tance  of  one  centimeter  from  A,  that  is,        Sx"- ^ 

the  surface  of  a  sphere  with  A  as  a  center  Fis-  26- 

and  a  radius  of  one  centimeter  is  a  unit  field.  From  Par.  61  there 
is  in  a  unit  field  one  line  of  force  per  square  centimeter  of  cross- 
section.  The  surface  of  this  sphere  is  4  ?r  square  centimeters  and 
since  each  contains  one  line  of  force,  4  TT  lines  of  force  radiate  from 
a  unit  charge. 

64.  Gauss'  Theorem. — If  around  one  or  more  charged  bodies 
a  closed  surface  be  drawn,  the  number  of  lines  of  force  which 
pierce  this  surface  is  equal  to  4  ?r  times  the  total  charge  included 
inside  the  surface.    This  follows  at  once  from  the  preceding  para- 
graph.   Each  unit  charge  has  4  -K  lines  of  force  radiating  from  it, 


48 


ELEMENTS  OF  ELECTRICITY. 


therefore  from  a  charge  q  there  would  radiate  4  irq  lines.  This  is 
one  way  of  expressing  Gauss'  Theorem,  a  principle  of  frequent 
employment  in  mathematical  discussions  of  electrostatic  problems. 
An  example  of  the  application  of  this  theorem  is  given  in  the  follow- 
ing paragraph. 

65.  Field  about  a  Uniformly- Charged  Sphere. — Let  0  (Fig.  27) 
be  the  center  of  a  uniformly-charged  sphere,  its  surface  density 

,*~ ~^N  being  5,  and  let  P  be  an  external  point  at 

/'  \         a  distance  D  from  this  center.    Through 

/  \       P  pass  a  sphere  with  0  as  a  center.    If  the 

charge  on  the  original  sphere  be  q,  then 
according  to  Gauss'  Theorem  4  irq  lines  of 
/       force  pierce  the  sphere  P.    The  area  of  the 
\^  /          sphere  P  is  4?rD2  and  the  distribution  of 

x^~ <-''  the  lines  of  force  is  uniform,  therefore  the 

Fig.  27.  number  of  lines  per  square  centimeter  is 

4  7rg/4  TrZ)2,  or  q/D2.  But  (Par.  61)  this  measures  the  intensity  of 
the  field  at  P  or,  in  other  words,  measures  the  force  with  which 
a  unit  charge  at  P  is  acted  upon,  whence  we  see  that  the  charge 
upon  a  uniformly-charged  sphere  acts  upon  external  points  as  if  it 
were  concentrated  at  the  center. 

If  the  external  point  be  indefinitely  near  the  surface  of  the  sphere 
the  force  exerted  will  be  q/R2.  Substituting  for  q  its  value  4  wR25, 
this  becomes  4?r5,  that  is,  the  field  very  near  the  surface  of  a 
charged  sphere  is  equal  to  4?r 
times  the  surface  density  of  the 
charge.  Coulomb  extended  this 
theorem  to  include  charged 
bodies  of  any  shape. 

66.  Field  near  a  Uniformly- 
Charged  Plane.— Let  AB  (Fig. 
28)  be  a  uniformly-charged 
plane,  its  surface  density  being 
5;  to  find  the  force  exerted  upon 
a  unit  positive  charge  at  P  at  a 
distance  D  from  the  plane.   Let 
PC  be  the  perpendicular  from 


Fig.  28. 


the  point  to  the  plane. 
y  -f  dy  describe  a  zone. 


With  C  as  a  center  and  radii  y  and 
The  area  of  the  zone  is  2  iry.dy.    The 


STATIC  ELECTRICITY.  49 

charge  upon  this  zone  is  2  iry.dy.5.    The  force  exerted  at  P  by 
this  charge  is 

2<n-y.d    , 
—  •  dy 

z 

The  normal  component  in  the  direction  PF  is 

2ir.d.y.COSa     -, 

— - —     —  .  dy 

z2 

The  integral  of  the  components  from  all  the  zones  will  give  the 
total  force.  To  prepare  the  above  expression  for  integration  cos  a 
and  z2  must  be  expressed  in  terms  of  y. 

From  the  figure  z2  =  D2  -f-  y2  and  cos  a  =  —  =     ,         == 

„  ,-       2irD.d.y      , 

Hence  df  =  •  ,  = .  dy 

v(D2+#2)3 

And  integrating          /  =  -   2/  +  C 

VD2  +  y2 

Taking  this  between  the  limits  y  =  oo  and  y  =  0 

/  =  2  w5  dynes 

In  this  expression  D  does  not  appear,  so  that  the  force  is  inde- 
pendent of  the  position  of  P  with  respect  to  the  plane.  If  the 
charged  plane  be  not  of  indefinite  extent,  the  expression  is  still 
approximately  correct  if  P  be  so  near  the  plane  that  the  dimen- 
sions of  the  plane  as  compared  to  this  distance  are  very  great. 

67.  Force  Exerted  upon  an  Internal  Point  by  a  Uniformly- 
Charged  Sphere. — Consider  a  uniformly-charged  insulated  sphere 
remote  from  other  bodies.  Let  P 
(Fig.  29)  be  any  point  within  such 
a  sphere  and  let  AB  be  any  line 
'  drawn  through  this  point.  Let  the 
tangents  at  A  and  B  represent  the 
traces  of  the  tangent  planes  at  those 
points.  The  line  AB  makes  equal 
angles  with  these  planes.  With  P 
as  a  vertex  describe  about  PB  as  Fig729. 

an  axis  a  slender  cone  EPF.  Pro- 
long its  elements  beyond  P  thus  describing  a  second  cone  GPH. 
Suppose  the  bases  of  these  cones  to  be  charged,  the  surface  density 
being  the  same  as  that  of  the  sphere.  They  are  similar  since  they 


50  ELEMENTS  OF  ELECTRICITY. 

have  equal  solid  angles  at  the  vertices  and  their  axes  make  equal 
angles  a  with  their  bases.  Let  PB  =  R,  PA=r,  the  area  of  the 
base  EF = S,  that  of  GH  =  s,  the  charge  on  EF  =  Q,  that  on  GH  =  q. 
The  force  exerted  by  Q  upon  a  unit  charge  at  P  is  Q  .  sin  a  /R2,  that 
exerted  by  q  is  q .  sin  a/r2.  The  charges  on  the  bases  of  these  cones 
being  of  the  same  surface  density 

Q : q  =  S  :s 

hence  the  above  expressions  are  proportional  to  S/R2  and  s/r2, 
respectively.  The  cones  being  similar 

S  :s  =  R2  :r2 

whence  S/R2  =  s/r2,  or  the  forces  exerted  upon  P  are  equal  and 
opposite. 

As  the  cones  are  made  smaller  their  bases  approach  coincidence 
with  the  surface  of  the  sphere.  The  whole  surface  of  the  sphere 
can  be  thus  divided  up  by  pairs  of  cones,  the  effects  of  the  charges 
upon  whose  bases  exactly  neutralize  one  another,  therefore,  the 
charge  upon  the  surface  exerts  no  force  at  an  internal  point. 

This  is  true  whatever  the  shape  of  the  conductor  or  surface 
distribution  of  the  charge  but  in  only  a  few  cases  can  the  conditions 
be  given  a  sufficiently  simple  mathematical  expression  to  permit 
of  ready  proof. 

This  fact  was  shown  experimentally  by  Faraday.  He  con- 
structed of  tin-foil  and  wire-netting  an  insulated  cubical  chamber 
into  which  he  entered  with  his  most  delicate  electroscopes.  The 
chamber  was  then  charged  so  highly  that  great  sparks  and  brush 
discharges  were  escaping  from  the  corners,  yet  his  instruments 
gave  no  indications  at  all. 

68.  The  Charge  Resides  on  the  Surface. — The  proof  of  the 
statement  in  Par.  38  that  the  charge  resides  on  the  surface  of  an 
insulated  conductor  follows  from  the  foregoing.  Suppose  that  we 
might  have  an  insulated  sphere  with  a  charge  distributed  uniformly 
throughout  its  substance.  This  charge  will  induce  on  surrounding 
objects  a  charge  of  the  opposite  kind.  The  attraction  between 
these  charges  will  cause  the  charge  in  the  sphere  to  move  out  to 
the  surface.  The  portions  of  the  charge  upon  the  surface  mutually 
repel  each  other  and  thus  spread  over  the  entire  exterior.  No 
part  of  the  charge  could  be  crowded  off  into  the  interior  of  the 
sphere  for  we  have  just  seen  that  the  charge  on  the  surface  exerts 
no  force  in  the  interior. 


STATIC  ELECTRICITY.  51 


CHAPTER  9. 
POTENTIAL. 

69.  Cause  of  Movement  of  Electric  Charges. — If  a  charged 
conductor  be  connected  to  the  earth  it  will  be  instantly  discharged. 
If  two  equal  insulated  spheres  containing  unequal  charges  be 
brought  into  contact  there  will  be  a  flow  from  the  greater  charge 
to  the  lesser  until  the  two  charges  are  equalized  and  equilibrium 
established.    If  the  spheres  be  of  unequal  size  yet  contain  equal 
charges  a  portion  of  the  charge  of  the  smaller  sphere  will  flow  to 
the  larger.    Finally,  if  these  unequal  spheres  have  charges  of  the 
same  surface  density  a  portion  of  the  charge  of  the  larger  will  flow 
to  the  smaller.     The  movement  is  therefore  not  entirely  deter- 
mined by  difference  in  the  size  of  the  conductors  or  by  inequality 
either  of  the  charges  or  of  surface  density  and  we  naturally  ask 
why  does  it  take  place.    It  is  produced  by  what  is  designated  a 
difference  of  electric  potential. 

70.  Physical   Analogues  of  Electric   Potential. — It  has  been 
remarked  that  one  of  the  reasons  why  the  study  of  electricity  is 
difficult  for  the  beginner  is  that  although  we  have  a  sense  of  weight, 
of  force,  of  direction,  of  velocity,  etc.,  we  are  devoid  of  an  electric 
sense  and  therefore  such  expressions  as  intensity  of  current, 
quantity  of  electricity,  electric  pressure,  electric  potential,  etc.,  are 
pure  abstractions.    To  convey  a  physical  conception  of  these  and 
to  aid  in  our  explanations  we  are  compelled  to  resort  to  analogies. 
In   explaining   electric  potential  it   is  frequently  compared   to 
temperature  and  to  water  level. 

Making  the  first  comparison,  it  is  not  size  or  shape  of  the  bodies 
or  quantity  of  heat  contained  but  difference  of  temperature  which 
determines  whether  heat  shall  pass  from  one  body  to  another,  the 
flow  taking  place  from  the  body  whose  temperature  is  the  higher. 
Thus  a  red-hot  nail  loses  heat  when  dipped  into  a  bucket  of  hot 
water,  although  the  water  may  contain  several  hundred  times 
more  units  of  heat  than  the  nail;  and  no  matter  how  they  differ  in 
size  there  is  no  net  transfer  of  heat  between  two  bodies  at  the  same 


52 


ELEMENTS  OF  ELECTRICITY. 


temperature.  So  with  electricity,  there  is  always  a  flow  when 
conductors  at  different  potentials  are  brought  into  contact,  the 
flow  (of  positive  electricity)  taking  place  from  the  conductor  of 
higher  potential,  and  there  is  no  flow  if  their  potentials  are  the 
same. 

Again,  if  two  vessels  containing  water  (Fig.  30)  are  connected 

by  a  pipe  there  will  be  a  flow 
from  the  vessel  in  which  the 
water  stands  at  the  higher  level 
and  this  is  irrespective  of  the 
actual  amounts  of  water  in  the 
two.  There  will  be  no  flow  if 
the  level  in  the  two  is  the 
same. 

These  analogies  can  not  be 
carried  too  far.     For  example, 
Flg-  30-  it  will  be  noted  that  a  change 

in  temperature  is  accompanied  by  a  change  in  volume  and  often 
by  a  change  in  state,  but  conductors  show  no  such  changes  when 
their  charges  are  varied. 

71.  Mechanical  Potential. — Consider  a  cord  (Fig.  31)  attached 
to  a  weight  W  and  running  over  a  pulley.  By  the  expenditure  of 
a  certain  amount  of  work  on  the  free  end  of 
the  cord  the  weight  can  be  raised  against 
the  force  of  gravity  through  a  vertical  dis- 
tance to  a  new  position  W.  In  this  new 
position  it  has  a  certain  amount  of  stored  up 
energy,  or  ability  to  do  work,  or  potentiality, 
for  if  the  free  end  of  the  cord  be  released  the 
weight  will  drop  back  to  W  and  in  doing  so 
will,  if  proper  mechanical  arrangements  be 
made  and  losses  by  friction  be  not  con- 
sidered, do  as  many  foot-pounds  of  work  as 
were  expended  originally  in  raising  it  to  the 
position  W. 

To  raise  it  to  W",  higher  than  W,  would 
require  a  greater  expenditure  of  energy  but 
also  its  potential  energy  at  W"  would  be  Fis-  3L 

correspondingly  greater  than  that  at  W.  We  see  then  that  its 
potential  energy,  or  for  brevity  its  potential,  varies  with  its  posi- 


w 


STATIC  ELECTRICITY.  53 

tion  with  respect  to  the  surface  of  the  earth  (more  strictly  with 
respect  to  the  center  of  gravity  of  the  earth)  and  at  every  different 
level  we  reach  it  has  a  corresponding  different  potential,  always 
exactly  measured  by  the  amount  of  work  expended  in  moving  the 
weight  from  the  surface  of  the  earth  to  that  level. 

Potential  as  thus  explained  is  not  an  inherent  property  of  the 
weight  for  in  its  various  changes  of  position  the  weight  in  itself 
does  not  change.  It  sometimes  becomes  desirable  to  compare  the 
potential  which  a  body  has  at  one  point  with  that  which  it  would 
have  at  another  point  and  we  therefore  speak  of  the  potential  of 
this  body  at  the  point,  or  simply  of  the  potential  of  the  point,  but 
points  in  space  have  no  potential  and  we  mean  the  potential  which 
the  body  when  moved  to  the  point  acquires  due  to  the  work  ex- 
pended in  the  movement. 

In  ordinary  mechanical  problems  the  force  of  gravity  at  any 
one  spot  is  considered  constant  and  the  potential  of  a  body  varies 
directly  with  the  vertical  distance  through  which  it  is  raised, 
therefore  it  suffices  to  give  the  height  and  this  height  in  feet  multi- 
plied by  the  weight  of  the  body  in  pounds  gives  the  foot-pounds 
by  which  the  potential  of  the  body  is  measured.  However,  should 
we  take  this  force  as  following  the  law  of  inverse  squares,  the 
amount  of  work  done  in  raising  a  body  one  foot  from  a  certain 
level  would  differ  from  the  amount  done  in  raising  this  same  body 
one  foot  from  some  other  level.  The  relative  potentials  of  the  two 
points  would  not  in  this  case  be  given  directly  by  their  heights  but 
by  the  work  expended  in  raising  the  same  weight  to  the  respective 
points.  Logically  therefore  we  would  compare  the  potentials  of 
points  by  comparing  the  work  expended  in  moving  a  unit  weight 
against  the  force  of  gravity  and  from  the  surface  of  the  earth  to 
the  respective  points. 

Theoretically,  since  it  is  neither  raised  nor  lowered,  no  work  is 
expended  in  moving  a  body  about  on  a  level.  Every  point  on  such 
a  surface  has  the  same  potential  and  it  could  therefore  be  called 
an  equipotential  surface.  A  unit  difference  of  potential  exists 
between  two  levels  when  a  unit  of  work  must  be  expended  in 
moving  a  unit  weight  from  one  to  the  other. 

72.  Electric  Potential. — We  arrive  at  a  definite  conception  of 
electric  potential  by  a  course  of  reasoning  parallel  to  the  foregoing. 
Suppose  A  (Fig.  32)  to  be  a  positively-charged  insulated  sphere 
and  B  a  small  sphere  with  a  unit  positive  charge.  B  will  be 


54  .  ELEMENTS  OF  ELECTRICITY. 

repelled  by  A,  the  force  varying  inversely  as  the  square  of  the 
distance.  At  an  infinite  distance  the  force  would  be  zero;  at  a 
great  distance  it  would  be  very  small  but  as  the  distance  be- 


G- 


B 

-o 


Fig.  32. 


comes  small  it  would  increase  rapidly.  Should  we  begin  with  B 
at  an  infinite  distance  and  push  it  up  towards  A  the  work  done  at 
first  would  be  very,  very  small  but  would  increase  as  we  ap- 
proached A  and  at  any  point  as  P  the  potential  would  be  exactly 
measured  by  the  work  expended  in  bringing  B  up  to  that  point. 
We  therefore  say  that  the  electric  potential  at  any  point  is  measured 
by  the  amount  of  work  that  must  be  spent  in  bringing  up  to  that 
point  from  an  infinite  distance  a  unit  of  positive  electricity.  Since 
we  use  the  C.  G.  S.  system,  electric  potential  as  thus  explained  is 
measured  in  ergs. 

Had  the  unit  charge  upon  B  been  negative,  its  potential  at  P 
would  have  been  negative  and  measured  by  the  work  expended  in 
pushing  it  back  to  an  infinite  distance. 

From  the  above  it  follows  that  the  difference  of  potential  between 
any  two  points  is  measured  by  the  work  expended  in  moving  a  unit 
of  positive  electricity  from  one  point  to  the  other.  Hence  also,  a  unit 
difference  of  potential  exists  between  two  surfaces  when  it  requires 
the  expenditure  of  one  erg  to  move  a  unit  positive  charge  from  one 
to  the  other. 

Parallel  to  the  case  of  mechanical  potential,  a  surface  every 
point  of  which  is  at  the  same  potential  is  an  equipotential  surface. 
Such  a  surface  is  that  of  any  conductor  in  which  no  electricity  is 
in  movement. 

73.  Zero  Potential. — Electricity  not  being  matter,  we  recognize 
it  and  measure  it  and  its  dynamical  properties  only  by  its  effects. 
If  all  bodies  about  us  were  at  the  same  potential  there  could  be  no 
movement  of  electricity  among  them  and  hence,  with  the  exception 
of  mutual  repulsion,  there  would  be  none  of  the  manifestations 
which  we  use  in  measurements.  Repulsion  of  like  charges  depends 
solely  upon  the  quantity  of  the  charges,  their  distance  apart  and 
the  medium  in  which  they  are  situated  and  would  be  the  same  no 
matter  how  high  or  how  low  their  common  potential,  therefore, 


STATIC  ELECTRICITY.  55 

there  is  no  means  of  determining  absolute  potential  but  only  rela- 
tive potential,  or,  as  it  is  usually  expressed,  "difference  of  potential." 
Fortunately,  there  is  no  need  of  knowing  the  absolute  potential, 
just  as  in  utilizing  water  power  it  is  not  necessary  to  know  the 
height  above  the  sea  but  it  is  essential  to  know  the  difference  of 
level.  A  point  at  an  infinite  distance  from  all  charged  bodies 
would  be  at  zero  potential  but  for  convenience  the  potential  of  the 
earth  is  taken  as  an  arbitrary  zero.  This  no  more  means  that  the 
absolute  potential  of  the  earth  is  zero  than  that  taking  the  melting 
point  of  ice  as  zero  implies  that  a  lower  temperature  does  not 
exist  or  the  taking  of  the  sea  level  as  zero  means  that  we  could  not 
go  to  greater  depths. 

74.  Potential  at  a  Point  due  to  a  Charge.— If  in  Fig.  33  the 
charge  at  P  be  unity,  that  at  A  be  Q  and  the  distance  between 


o 


£> 


Fig.  33. 

A  and  P  be  x  centimeters,  the  force  at  P  will  be  Q/x2  dynes, 
the  work  performed  by  the  unit  charge  in  moving  from  P  to  P', 
a  distance  dx,  will  be 

I'd*  ergs 

and  the  total  work  performed  in  moving  from  P  to  an  infinite  dis- 
tance will  be 

'**-!«• 

x  =  x 

Hence  the  work  expended  in  the  opposite  direction  in  moving 
the  unit  charge  from  infinity  up  to  P  will  also  be  Q/x  ergs.  But 
from  Par.  72,  this  measures  the  potential  at  the  point  P.  There- 
fore, the  potential  at  any  point  due  to  a  charge  is  equal  to  the 
charge  divided  by  the  distance  between  the  charge  and  the 
point. 

An  important  corollary  of  the  foregoing  is  that  the  potential 
at  any  point  due  to  more  than  one  charged  body  is  equal  to 
the  sum  of  the  potentials  at  that  point  due  to  the  bodies  taken 
separately. 


56  ELEMENTS  OF  ELECTRICITY. 

75.  Expression  for  Electric  Force. — An  expression  for  the  elec- 
tric force  acting  upon  charged  bodies  may  be  deduced  as  follows: 
Work  is  equal  to  force  X  path,  hence 

.  work 

force  =  — TT- 

path 

The  work  performed  in  pushing  a  unit  of  positive  electricity 
from  one  point  to  another  is  equal  to  the  product  of  the  electric 
force  by  the  distance  between  the  points.  But  from  what  we 
have  seen  above  (Par.  72)  this  work  measures  the  difference  of 
potential  between  the  two  points,  therefore  the 

,       .     -  difference  of  potential 

~  distance  between  the  points 

This  is  correct  only  on  the  assumption  that  the  force  has  been 
constant  throughout  the  path  but  it  is  the  exception  when  such 
is  the  case.  However,  the  nearer  we  take  the  two  points  together 
the  nearer  we  get  to  the  true  value  of  the  force,  hence,  designating 
the  difference  of  potential  between  the  two  points  by  V  and  the 
distance  between  them  by  x  we  have  at  the  limit 

,  .    ,  dV 

electric  force  =  -j— 

ax 

or  the  electric  force  at  any  point  is  equal  to  the  rate  of  change  at  that 
point  of  potential  per  unit  of  length. 

76.  Electro-Motive  Force. — In    the    example    of    mechanical 
potential  in  Par.  71  above,  if  the  cord  be  only  partly  paid  out  the 
weight  will  fall  a  corresponding  distance,  the  tendency  always 
being  for  the  body  to  move  from  a  point  of  high  potential  to  one 
of  lower.    In  the  case  of  electricity  there  is  a  like  tendency,  and  the 
insulation  of  a  charged  body  may  be  regarded  as  analogous  to  the 
cord  since  it  restrains  the  charge  from  flowing  from  the  body  to 
another  of  lower  potential.    If  the  charged  body  be  connected  to  a 
body  of  lower  potential  it  is  analogous  to  paying  out  the  cord,  and 
if  it  be  connected  through  a  conductor  to  the  earth  the  effect  is 
analogous  to  cutting  the  cord. 

In  the  illustration  of  electric  potential,  if  the  little  sphere 
pushed  up  from  an  infinite  distance  and  containing  the  unit  posi- 
tive charge  be  released  it  will  be  pushed  back,  the  charge  and  the 
sphere  both  moving.  If  instead  of  releasing  the  sphere,  it  be  con- 
nected, say  through  a  conducting  wire,  with  the  earth,  the  charge 
alone  will  be  pushed  back  along  the  wire  to  a  point  of  zero  poten- 


STATIC  ELECTRICITY.  57 

tial.  In  this  case  no  movement  of  matter  is  involved  but  only  of 
the  charge.  If  new  charges  be  supplied  to  the  little  sphere  as  fast 
as  the  previous  charges  flow  away,  it  will  be  kept  at  a  constant 
potential  and  the  successive  charges  following  along  the  wire  will 
constitute  a  continuous  stream.  This  is  what  is  known  as  current 
electricity  and  is  discussed  later. 

Mechanical  force  is  defined  as  that  which  moves  or  tends  to 
move  or  tends  to  produce  a  change  of  motion  in  matter.  In  the 
case  of  the  movement  of  electricity  however  no  matter  is  involved. 
The  first  force  might  therefore  be  named  "matter-motive  force/' 
the  second  in  centra-distinction,  is  named  "electro-motive  force," 
and  can  be  defined  as  that  force  which  moves  or  tends  to  move 
electricity.  It  is  represented  in  symbols  as  E.  M.  F. 

77.  Practical    Unit    of   Electro -Motive    Force. — Reverting   to 
our  comparison  of  potential  to  water  level,  the  flow  of  water  is 
produced  by  a  force  and  this  force  is  the  pressure  due  to  the  "head" 
or  difference  of  level  between  the  surface  of  the  water  and  the  out- 
let.   So  the  flow  of  electricity  is  produced  by  the  electro-motive 
force  which  in  turn  is  caused  by  the  difference  of  potential  between 
the  two  ends  of  the  path.    The  difference  of  level  in  the  case  of 
water  is  measured  in  feet,  the  corresponding  pressure  is  measured 
in  pounds  per  square  inch,  and  for  any  given  difference  in  level 
the  pressure  in  pounds  per  square  inch  may  be  obtained  by  multi- 
plying this  difference  expressed  in  feet  by  the  factor  .434.    In  the 
case  of  water  the  cause  and  effect  are  so  closely  connected  that  we 
often  hear  such  expressions  as  "a  pressure  of  30  feet." 

The  practical  unit  of  electric  pressure  or  of  electro-motive  force 
is  called  the  volt  and  will  be  defined  later.  Difference  in  potential 
expressed  in  ergs  is,  for  reasons  given  later,  converted  into  the 
corresponding  electro-motive  force  in  volts  by  multiplying  by  300. 
Similar  to  the  case  of  water  it  has  become  usual  to  confound  cause 
and  effect  and  it  is  customary  to  speak  of  a  difference  of  potential 
of  so  many  volts.  Some  writers  even  go  to  the  extent  of  stating 
that  difference  of  potential  and  electro-motive  force  are  two  names 
for  one  and  the  same  thing.  In  view  of  this,  insistence  upon  the 
distinction  becomes  academic  and  of  no  practical  importance  and 
hereafter  will  not  be  dwelt  upon. 

78.  Summary. — The   gist   of   the   preceding   discussion   upon 
potential  is  that  whenever  a  charge  of  electricity  is  produced,  it 


58  ELEMENTS  OF  ELECTRICITY. 

may  be  regarded  as  brought  up  from  infinity  or  from  a  point  of 
zero  potential  and  whenever  a  difference  of  potential  is  developed, 
the  charge  must  either  have  been  pushed  against  a  repulsion  or 
pulled  against  an  attraction.  In  either  case,  just  like  a  spiral 
spring  which  has  been  compressed  or  extended,  it  has  a  tendency 
to  fly  back  and  can  be  retained  in  its  position  only  by  a  continua- 
tion of  the  push  or  pull  or  by  the  interposition  of  an  insulator. 
The  more  the  mechanical  or  chemical  energy  expended  in  bringing 
up  the  charge,  the  greater  its  potential  energy  or  the  greater  its 
tendency  to  fly  back  when  released.  The  potential  of  the  charge 
is  measured  by  the  work  in  ergs  spent  in  bringing  up  a  portion  of 
it  equal  to  one  positive  unit.  The  force  with  which  the  unit 
charge  when  released  would  be  pushed  back,  or  the  electro-motive 
force,  is  measured  in  units  called  volts  whose  number  is  obtained 
by  multiplying  the  ergs  by  300. 


STATIC  ELECTRICITY. 


59 


CHAPTER  10. 

ELECTROSTATIC   CAPACITY. 

79.  Electrostatic  Capacity. — At  several  points  in  the  preceding 
pages  reference  has  been  made  to  electric  capacity.  The  word 
"capacity"  in  its  application  to  electricity  is  used  in  a  sense  quite 
different  from  its  ordinary  acceptance  and  necessarily  so,  as  the 
following  will  show.  The  capacity  of  a  vessel  is  the  volume  which 
it  will  contain  and  is  fixed  once  for  all.  If  by  the  capacity  of  a 
conductor  we  meant  the  amount  of  electricity  which  could  be  im- 
parted to  it,  the  term  would  be  indefinite  for  as  conditions  vary 
the  same  conductor  could  contain  very  different  amounts.  Re- 
sorting to  analogy,  conductors  can  be  compared  to  vertical 


Fig.  34. 

cylindrical  vessels  differing  in  cross-section  and  of  indeterminate 
height  (Fig.  34).  The  amount  of  water  which  could  be  placed  in 
any  of  these  vessels  would  depend  upon  the  cross-section,  upon 
the  height  to  which  the  inflowing  liquid  could  be  raised  by  the 
supply  pump  and  also  upon  the  strength  of  the  material,  that  is, 
the  height  to  which  the  cylinder  could  be  filled  before  the  pressure 
caused  the  bottom  or  sides  to  yield.  Hence,  keeping  the  cross- 
section  constant,  the  capacity  might  be  varied  by  using  a  more 
powerful  pump  or  a  stronger  material  for  the  vessel.  The  only 
basis  of  comparison  in  terms  of  contents  would  therefore  be  the 
amount  of  water  that  would  cause  the  pressure  per  square  inch 
on  the  bottom  to  increase  a  definite  amount,  or,  since  this  pressure 
varies  directly  as  the  head,  the  amount  of  water  that  would  raise 
the  level  in  the  vessel  a  certain  distance,  say  one  foot.  If  one 


60  ELEMENTS   OF  ELECTRICITY. 

gallon  raises  the  level  one  foot  in  a  certain  cylinder  and  it  requires 
two  gallons  to  do  the  same  in  another,  the  second  cylinder  may  be 
said  to  have  twice  the  capacity  of  the  first.  The  same  amount  of 
water  will  raise  the  level  more  quickly  in  a  small  cylinder  than  in 
a  large  one. 

If  various  insulated  conductors  be  connected  to  a  charged  body 
of  higher  potential,  electricity  will  flow  from  the  source  into  them 
until  a  common  potential  is  reached.  The  small  conductors  will 
receive  least  for  less  is  required  to  raise  their  potential  to  the  com- 
mon level.  Upon  reaching  the  common  potential  the  flow  will 
cease  but  should  the  potential  of  the  source  be  increased  the  flow 
will  again  begin  and  continue  until  a  new  common  potential  is 
reached.  This  can  be  continued,  the  potential  of  the  conductors 
steadily  rising,  but  finally  the  strain  on  the  medium  surrounding 
the  conductors  becomes  so  great  as  to  overcome  its  dielectric 
strength  (see  Par.  93),  there  is  a  breakdown  and  a  discharge 
occurs.  Hence  the  total  quantity  of  electricity  which  can  be 
transferred  to  a  conductor,  besides  varying  with  the  size  of  the 
conductor  also  depends  upon  the  difference  of  potential  between 
the  conductor  and  the  source  of  electricity  and  upon  the  dielectric 
strength  of  the  surrounding  medium  and  is  therefore  indefinite. 
On  the  other  hand,  the  capacity  of  a  conductor  is  measured  by  the 
quantity  of  electricity  which  must  be  imparted  to  it  to  raise  its 
potential  one  unit,  and  is  perfectly  fixed  and  definite. 

If  a  charge  Q  imparted  to  a  body  raises  its  potential  V  units, 
then  a  charge  Q/V  would  raise  its  potential  one  unit.  But,  by 
the  preceding  definition,  this  is  the  measure  of  the  capacity  of  the 
body,  and  representing  the  capacity  by  K,  we  have  the  relation 
between  these  three  quantities  given  by  the  expression 

K      $ 
=  V 

80.  Capacity  of  a  Sphere. — The  capacity  of  most  bodies  must 
be  determined  by  actual  measurement  but  for  a  few  of  simple 
geometrical  form  it  may  be  calculated.  The  capacity  of  a  sphere 
may  be  determined  as  follows.  In  Par.  74  it  was  shown  that  the 
potential  at  a  point  due  to  a  charge  Q  at  a  distance  x  from  the 
point  is  Q/x.  If  the  charge  Q  be  upon  the  surface  of  a  sphere  it 
acts  as  if  concentrated  at  the  center  of  the  sphere  (Par.  65),  and 
hence  the  distance  between  the  charge  and  the  point  must  be 


STATIC  ELECTRICITY.  61 

measured  from  the  center  of  the  sphere.  Therefore,  the  potential 
of  a  point  infinitely  near  the  surface  of  the  sphere  (that  is,  the 
potential  of  the  sphere  itself)  is  V  =  Q/R.  In  other  words,  the 
potential  of  a  sphere  varies  directly  as  the  charge  and  inversely  as 
the  radius.  In  the  above  expression  if  V  =  1,  Q  must  be  equal  to 
R,  that  is,  to  maintain  unit  potential  as  R  varies,  Q  must  vary  in 
the  same  ratio  and  preserve  numerical  equality  with  R.  We  also 
see  that  the  capacity  of  a  sphere  varies  directly  as  its  radius.  This 
may  be  shown  directly  by  substituting  in  the  expression  for 
capacity,  K=  Q/V,  the  above  value  V=  Q/R,  whence  we  obtain 

K  =  R 

or  the  number  of  units  of  electricity  required  to  raise  the  potential 
of  a  sphere  by  unity  is  equal  to  the  number  of  centimeters  in  the 
radius  of  the  sphere.  A  unit  charge  would  therefore  raise  by  unity 
the  potential  of  a  sphere  of  one  centimeter  radius  and  such  a 
sphere  is  said  to  have  unit  capacity. 

Certain  interesting  consequences  follow  from  the  foregoing,  two 
of  which  we  shall  now  notice. 

81.  Case  of  Two  United  Spheres. — If  two  unequal  spheres  be 
placed  in  contact  or  be  joined  by  a  conductor  and  a  charge  be  im- 
parted to  either  they  will  come  to  a  common  potential,  or  will 
share  the  charge  in  proportion  to  their  capaci- 
ties, which,  from  the  preceding  paragraph,  is 

also  in  proportion  to  their  radii.  Suppose  the 
radius  of  A  (Fig.  35)  to  be  twice  that  of  B,  the 
charge  upon  A  will  be  twice  the  charge  upon  B.  Flg*  3o> 

The  surfaces  of  these  spheres  being  to  each  other  as  the  squares  of 
their  radii,  the  surface  of  A  is  four  times  that  of  B.  The  surface 
density  of  the  charge  on  A  is  therefore  as  2/4,  that  of  the  charge 
on  B  is  as  1/1,  or  the  surface  density  on  B,  although  B  has  the 
smaller  charge,  is  twice  that  on  A.  If  B  is  very  small  as  compared 
to  A,  its  surface  density  will  become  very  great  and  we  have  seen 
(Par.  41)  that  if  the  surface  density  exceeds  20  units  per  square 
centimeter  a  discharge  will  take  place.  This  is  the  explanation 
of  the  action  of  points  already  described  (Par.  42). 

82.  Case   of  Two   Coalescing    Spheres. — Suppose   two   equal 
charged  spheres,   A  and  B   (Fig.  36),  should  coalesce  produc- 
ing a  resultant  sphere  C.     If  the  radius  of  A  be  r  and   that 


62  ELEMENTS  OF  ELECTRICITY. 

of   C  be   R,   since   the  volume  of  a  sphere  =  firr3  we   have 


Hence  #3  =  2r3  or  R  =  ^/2.r  =  1.26r. 

Hence,  since  the  capacity  of  a  sphere  varies 
directly  with  its  radius,  it  will  require  1.26  times 
Fig.  36.  as  large  a  charge  to  raise  the  potential  of  the 
sphere  C  one  unit  as  is  required  to  raise  that  of  A  or  of  B  one  unit. 
But  by  the  coalescing  of  the  spheres  C  receives  twice  as  great  a 
charge  as  A  or  B,  or  .74  times  more  than  necessary  to  bring  it  to 
the  same  potential,  and  hence  its  potential  is  greater  than  that 
of  A  or  B. 

It  is  known  that  evaporation  is  accompanied  by  the  production 
of  electricity,  the  vapor  being  charged.  As  the  vapor  begins  to 
condense,  the  molecules  unite  into  globules,  these  microscopic 
globules  into  larger  ones  and  these  into  still  larger  ones  until  drops 
of  rain  result.  By  this  coalescing  the  potential  is  enormously  in- 
creased until  a  final  point  is  reached  when  a  disruptive  discharge, 
a  flash  of  lightning,  takes  place.  This  is  an  explanation  which  has 
been  advanced  to  account  for  thunder  storms. 

83.  Condensers.  —  In  the  discussion  of  capacity  in  Pars.  79  and 
80  above,  the  conductors  were  supposed  to  be  remote  from  all 
other  bodies.  Should  the  conductor  to  which  the  charge  is  given 
be  near  to  a  second,  this  last  being  connected  to  the  earth,  a  very 
different  state  of  affairs  will  result.  A  charge  imparted  to  the  first 
will  repel  from  the  second  into  the  earth  a  similar  and  almost  equal 
charge  and  induce  and  attract  into  it  an  opposite  and  almost  equal 
charge.  In  Par.  74  it  was  stated  that  the  potential  at  a  given 
point  due  to  more  than  one  charged  body  is  equal  to  the  sum  of 
the  potentials  at  that  point  due  to  the  bodies  taken  separately. 
The  potential  of  the  first  body  is  therefore  the  sum  of  the  potentials 
due  to  its  own  charge  and  to  the  induced  charge  and  these  being  of 
opposite  signs  the  resultant  potential  is  much  less.  The  potential 
being  less,  a  greater  charge  is  required  to  raise  the  potential  of  the 
first  body  a  certain  amount  than  was  required  when  this  body  was 
remote  from  all  others,  in  other  words,  its  capacity  is  increased. 
We  see  then  that  the  capacity  of  a  conductor  is  increased  by  the 
proximity  of  another  which  is  earth  connected,  and  since  a  greater 
charge  can  now  be  given  to  it  before  a  given  change  of  potential  is 
produced,  such  an  arrangement  is  called  a  condenser.  The  earliest 


STATIC  ELECTRICITY.  63 

form  of  a  condenser  was  the  Leyden  Jar  which  we  shall  now  con- 
sider. 

84.  Invention  of  the  Leyden  Jar. — The  invention  of  the  Leyden 
jar  is  in  dispute,  the  merit  having  been  claimed  for  three  or  more 
persons.    Priestly,  noted  as  the  discoverer  of  oxygen,  has  left  a 
contemporaneous  account  of  the  event  which  is  in  substance  as 
follows:     Dr.  Muschenbroek  of  Leyden  in  experimenting  with 
static  electricity  was  much  troubled  by  the  rapidity  with  which 
his  conductors  lost  their  charge  and  ascribed  this  loss  to  some 
"effluvium"  in  the  surrounding  air.    He  therefore  thought  to  pro- 
tect his  charged  body  by  surrounding  it  by  a  non-conducting 
vessel  which  would  shield  it  from  the  atmosphere.    To  test  this, 
he  poured  some  water  into  a  glass  jar  and  holding  the  jar  in  his 
left  hand  he  led  a  charge  into  the  water  by  a  wire  attached  to  the 
prime  conductor  of  the  crude  machine  he  was  using.    After  giving 
the  handle  of  the  machine  a  few  turns  he  attempted  to  disengage 
with  his  right  hand  the  wire  from  the  prime  conductor  but  as  he 
touched  it  there  was  a  flash  and  he  was  subjected  to  a  strong  con- 
vulsive shock.    In  a  letter  describing  this  experience  he  states  that 
he  felt  himself  struck  in  his  arms,  shoulders  and  breast  so  that  he 
lost  his  breath  and  was  two  days  before  he  recovered  from  the 
effects  of  the  blow  and  the  terror.     He  added  that  he  would  not 
take  a  second  shock  for  the  whole  Kingdom  of  France. 

This  experiment  was  quickly  repeated  by  other  investigators. 
It  was  soon  found  that  no  appreciable  charge  could  be  given  to 
the  jar  unless  it  were  held  in  the  hand  and  that  the  amount  of  the 
charge  varied  with  the  amount  of  the  surface  touched  by  the  hand. 
This  led  to  the  substitution  of  a  metallic  outer  covering.  It  was 
next  discovered  that  the  charge  did  not  increase  in  proportion  to 
the  amount  of  water  in  the  jar  but  rather  in  proportion  to  the  area 
of  the  surface  wetted  and  this  led  to  the  substitution  of  a  lining  of 
tin-foil.  Finally,  it  was  found  that,  other  conditions  being  the 
same,  the  thinner  the  jar  the  greater  the  charge  that  it  could  be 
given. 

85.  The  Leyden   Jar. — The  usual  form  consists  of  a  wide- 
mouthed  glass  jar  (Fig.  37)  coated  inside  and  out  for  about  two- 
thirds  of  its  height  with  tin-foil.     It  is  closed  with  a  stopper  of 
insulating  material  through  which  passes  a  brass  rod  terminating 
above  in  a  knob  and  below  in  a  small  chain  which  dangles  long 
enough  to  touch  the  tin-foil  lining. 


64 


ELEMENTS  OF  ELECTRICITY. 


To  charge  the  jar,  the  outer  coating  must  be  connected  to  earth 
either  by  being  placed  upon  a  wire  or  chain,  one  end  of  which  is 
grounded,  or  by  being  held  in  the  hand  and  afforded  a  path  through 
the  body.  The  knob  is  then  held  to  the  prime  conductor  of  a 
machine  in  operation  and  in  a  very  short  while  the  jar  is  charged. 


Fig.  37. 

The  inner  lining  receives  the  same  kind  of  charge  as  is  generated 
by  the  machine;  the  outer  coating  receives  a  charge  of  the  opposite 
kind.  It  can  not  be  charged  indefinitely.  As  we  continue  to  turn 
the  handle  of  the  machine,  a  point  will  be  reached  when  the  tension 
between  the  two  opposite  charges  becomes  so  great  that  either  the 
glass  of  the  jar  will  be  pierced  or  else  a  discharge  will  occur  by  the 
charge  creeping  up  the  surface  of  the  glass  to  the  mouth  of  the  jar 
and  thence  down  to  the  outer  coating. 

A  jar  once  charged  will  remain  so  for  some  time.  The  inner  and 
outer  charges  are  mutually  bound  and  can  not  be  removed  by 
touching  the  inner  or  the  outer  coatings  separately,  but  if  they  be 
touched  simultaneously  by  any  body  which  will  afford  a  path 
between  the  two  charges,  the  jar  is  instantly  discharged.  Since 
the  effect  of  the  discharge  through  the  body  is  disagreeable  and 
may  be  dangerous,  use  is  made  of  a  discharger,  a  knobbed  con- 
ductor, hinged  at  the  middle  like  a  pair  of  tongs  and  furnished 
with  glass  handles.  It  is  held  by  the  handles  while,  as  shown  in 
Fig.  37,  one  knob  is  touched  to  the  knob  of  the  jar,  the  other  to 
the  outer  coating. 


STATIC  ELECTRICITY. 


65 


86.  Explanation  of  Leyden  Jar. — Reflection  and  experiment 
will  show  that  the  jar  form  of  this  apparatus  is  unimportant  and 
that  the  essential  parts  are  two  sheets  of  conducting  material 
separated  by  a  thin  non-conducting  sheet.  A  window-pane  set 
on  edge  with  a  sheet  of  tin-foil  pasted  in  the  center  on  each  side  is 
as  efficient  as  a  jar  of  equal  area  of  glass  and  foil.  Such  an  ar- 
rangement was  called  by  Franklin  a  "fulminating  pane."  If  more 
rigid  metal  sheets  be  substituted  for  the  tin-foil  and  if  they  be 
mounted  upon  an  insulating  support,  the  glass  may  be  replaced 
by  a  thin  layer  of  air  and  the  apparatus  is  then  called  an  air 
condenser. 

The  arrangement  shown  in  Fig.  38  enables  us  to  examine  the 
action  of  a  condenser  under  various  conditions.  A  and  B  are 


-  + 

-  + 

-  4- 

-  + 


B 


Fig.  38. 

vertical  metallic  plates  mounted  upon  insulating  stands  by  which 
the  distance  between  them  may  be  varied.  A  is  connected  by  a 
chain  or  wire  to  the  earth  and  B  is  connected  to  the  prime  con- 
ductor C  of  a  machine  which  we  shall  suppose  is  positively  charged. 
At  first  let  A  be  remote  from  B.  C  being  at  a  higher  potential 
than  B,  a  charge  will  flow  into  B  and  B  and  C  will  reach  a  common 
potential.  If  now  A  be  moved  up  near  B,  the  charge  on  B  will 
induce  a  negative  charge  on  A  and  repel  a  positive  charge  into  the 
earth.  The  potential  of  B  is  the  sum  of  that  due  to  its  own  charge 
and  that  due  to  the  charge  on  A.  This  last  being  negative,  the 
potential  of  B  is  lowered  and  more  charge  will  flow  into  B  from  C 
until  B  and  C  are  again  brought  to  a  common  potential.  Each 
additional  quantity  that  flows  into  B  from  C  will  induce  a  corre- 


66 


ELEMENTS  OF  ELECTRICITY. 


spending  quantity  of  negative  electricity  in  A,  the  joint  effect  of 
the  two  being  to  reduce  the  potential  to  which  B,  if  remote  from 
A,  would  be  raised  and  thus  a  much  greater  charge  can  be  given 
to  B  than  would  otherwise  have  been  possible. 

If  the  chains  be  now  disconnected  from  A  and  from  B  and  if  A 
and  B  be  drawn  apart,  the  pith  balls  attached  to  the  supports  will 
be  repelled  more  strongly,  as  if  A  and  B  had  received  greater 
charges.  This  may  be  explained  either  by  the  fact  that  as  the 
distance  between  A  and  B  increases,  the  two  charges  are  not  so 
strongly  bound  mutually  and  tend  to  spread,  or  that  the  effect  of 
the  negative  charge  on  A  upon  the  potential  of  B  becomes  less 
and  the  potential  of  B  increases. 

If  A  and  B  be  pushed  closer  together  the  pith  balls  will  again 
drop  down.  The  conclusion  is  that  other  things  being  equal  the 
capacity  of  a  condenser  varies  inversely  as  the  distance  apart  of 
the  conducting  surfaces. 

87.  Location  of  Charge  of  a  Condenser. — In  the  course  of 
some  experiments  with  a  Ley  den  jar  which  contained  water 
instead  of  an  inner  coating  of  tin-foil,  Franklin,  having  charged 
the  jar,  poured  out  the  water  into  another  vessel  and  expected 


Fig.  39. 

thus  to  obtain  the  liquid  highly  charged.  His  tests  however  giving 
no  marked  results,  he  thought  to  repeat  the  experiment  and  poured 
fresh  water  into  the  jar  when,  to  his  surprise,  he  found  the  jar  to  be 
almost  as  highly  charged  as  in  the  beginning.  He  concluded  that 
the  charge,  since  it  remained  behind,  could  not  have  been  dis- 
tributed in  the  liquid  and  must  have  been  spread  over  the  surface 
of  the  glass.  To  demonstrate  this  he  constructed  a  jar  with 
movable  coatings  (Fig.  39).  After  this  jar  has  been  charged,  the 


STATIC  ELECTRICITY.  67 

inner  coating  C  may  be  lifted  out  by  inserting  a  glass  rod  in  the 
hook  and  then  the  glass  B  may  be  taken  out  of  the  outer  coating 
A.  C  and  A  may  now  be  shown  to  have  no  appreciable  charge 
either  separately  or  together,  but  if  the  jar  be  reassembled  it  will 
give  almost  as  large  a  spark  as  it  would  have  given  just  after 
charging.  The  coatings  therefore  serve  merely  as  paths  by  which 
the  charge  is  conducted  about  over  the  surface  of  the  glass  and 
the  surface  of  this  glass  is  the  seat  of  the  charge.  This  may  also 
be  shown  with  the  condenser  represented  in  Fig.  38  if  a  sheet  of 
some  non-conducting  material  be  inserted  between  the  plates  but 
not  if  the  medium  between  be  air  or  gas. 

We  saw  in  Par.  60  that  every  electric  field  consists  of  non- 
conductors and  is  bounded  by  conductors,  and  elsewhere  (Par.  57) 
it  was  stated  that  the  medium  within  the  limits  of  a  field  is  not 
passive  or  inert  but  takes  part  in  the  transmission  of  the  electrical 
effects  and  is  subjected  to  certain  mechanical  strains.  Of  this 
there  are  many  proofs.  For  example,  if  a  beam  of  polarized  light 
be  passed  through  a  piece  of  glass  not  under  mechanical  strain  no 
effect  is  produced  but  should  the  glass  be  strained,  then  the  beam 
on  emergence  will,  if  allowed  to  fall  upon  a  white  surface,  produce 
certain  color  effects.  Such  a  beam  passed  through  a  piece  of  glass 
placed  in  an  electrical  field  will  reveal  the  presence  of  strains* 
Again,  if  shortly  after  a  Leyden  jar  has  been  discharged,  the  dis- 
charger be  again  applied,  an  additional  spark  may  be  obtained  and 
sometimes  even  a  third.  The  production  of  this  residual  charge 
may  be  hastened  by  tapping  the  jar.  This  is  sometimes  explained 
by  saying  that  a  portion  of  the  charge  has  soaked  into  the  glass 
but  it  is  perhaps  better  to  say  that  the  material  has  been  strained 
so  near  its  elastic  limit  that,  like  an  overloaded  spring  when  the 
load  is  removed,  it  does  not  return  instantly  to  its  primary  posi- 
tion. There  is  no  residual  charge  in  an  air  condenser.  Also  when 
a  Leyden  jar  is  charged  and  discharged  rapidly  a  number  of  times 
the  glass  grows  warm  just  as  does  a  spring  when  rapidly  com- 
pressed and  extended.  Finally,  the  discharge  of  a  jar,  while 
apparently  a  simple  phenomenon,  is  in  reality  complex  and  by  the 
application  of  instantaneous  photography  to  the  image  of  the 
spark  in  a  rapidly  rotating  mirror  (Par.  688)  it  can  be  shown  to  be 
in  the  nature  of  an  oscillation,  sparks  of  decreasing  intensity  passing 
back  and  forth  just  as  a  released  spring  vibrates  with  decreasing 
amplitude  back  and  forth  across  its  neutral  position.  This,  with 


68 


ELEMENTS  OF  ELECTRICITY. 


the  proof  that  the  charge  of  a  Leyden  jar  lies  on  the  surface  of  the 
glass,  would  seem  to  justify  us  in  saying  that  the  real  seat  of  the 
charge  is  along  the  bounding  surfaces  of  the  non-conductor  en- 
closed within  the  limits  of  the  field  and  that  the  energy  of  the  charge 
is  due  to  the  stresses  set  up  in  this  medium;  the  conductor  there- 
fore plays  a  minor  part. 

88.  Capacity  of  a  Spherical  Condenser. — The  capacity  of  a 
condenser  is  measured  by  the  quantity  of  electricity  that  must  be 
imparted  to  one  plate  (the  other  plate  being 
connected  to  the  earth  or  "grounded"  and 
hence  at  zero  potential)  to  raise  its  potential 
unity.  For  many  condensers  the  capacity 
must  be  measured,  for  others  it  may  be  calcu- 
lated. For  example,  let  it  be  required  to  deter- 
mine the  capacity  of  a  spherical  condenser. 
Let  A  (Fig.  40)  be  a  metallic- sphere  surrounded 
by  the  metallic  sphere  B  and  separated  from  B 
by  a  thickness  of  air  t.  If  R  be  the  radius  of  A, 
that  of  B  is  R'  =  R+t.  Let  B  be  connected  to 
earth.  The  potential  of  B  is  therefore  zero.  If 
a  charge  Q  be  imparted  to  A,  a  charge  —  Q  will 


B 


Fig.  40. 


be  induced  upon  the  inner  surface  of  B.  The  potential  of  A  due 
to  its  own  charge  is  Q/R  (Par.  80) ;  the  potential  of  A  due  to  the 
charge  on  B  is 

Q 

"irn 

The  resultant  potential  of  A  is  (Par.  74) 


= 
R 

And  since  (Par.  79) 


R  +  t     R(R  +  0 
'  =  Q/V 

QRR'      RR' 


RR' 


Qt        ~F~ 

or  the  capacity  varies  directly  as  the  area  of  the  conducting  sur- 
faces and,  as  was  shown  in  Par.  86,  inversely  as  the  thickness  of 
the  layer  of  air  separating  these  surfaces. 

A  conducting  sphere  of  one  centimeter  radius  has  unit  capacity, 
that  is,  one  electrostatic  unit  raises  its  potential  unity.  If  it  be 
surrounded  by  a  concentric  conducting  sphere  connected  to  the 


STATIC  ELECTRICITY. 


69 


earth  and  leaving  an  air  space  of  one  millimeter  (1/25  of  an  inch) 
between  the  two,  its  capacity  becomes  11,  that  is,  eleven  units  of 
electricity  must  now  be  imparted  to  it  to  raise  its  potential  unity. 
The  appropriateness  of  the  term  "condenser"  is  hence  apparent. 

89.  Capacity  of  a  Plate  Condenser. — Let  AB  (Fig.  41)  be  a 
plate  of  glass  of  thickness  t  upon  the  opposite  sides  of  which  are 
pasted  equal  circular  discs,  E  and  F,  of  tin-foil,  one  of  which,  as 
F,  is  connected  to  the  earth.  Let  the  radius  of  these  discs  be  R. 
If  now  a  positive  charge  be  imparted  to  E  it  will  induce  and  bind 
an  equal  opposite  charge  upon  F  and  repel  into  the  A 

earth  an  equal  positive  charge.  If  the  surface 
density  of  E  be  5,  that  of  F  (as  shown  in  Par.  62) 
will  be  —  8.  A  unit  positive  charge  placed  between 
E  and  F  will  be  repelled  from  E  with  a  force  of 
j .  2  7r5  dynes  (Pars.  66  and  55)  and  attracted  to  F 
with  an  equal  force,  the  total  force  being  ^Awd. 
The  work  done  in  moving  this  unit  charge  from 
F  to  E,  a  distance  t,  is  ^ .  Airdt.  According  to  what 
was  shown  in  Par.  72,  this  measures  the  difference  of  „ 

potential  between  F  and  E,  hence 


W//7/////, 
Fig.  41. 

F  being  connected  to  earth,  its  potential  V"  is  zero,  hence  the 
potential  of  E  is 


But  (Par.  79)  the  capacity  K  =  Q/V,  hence 
K-k     Q 

J\.    —    /v  • 


The  face  of  the  disc  E  is  nR2,  the  charge  upon  it  is  wR2d. 
stituting  this  for  Q  in  the  above  expression  we  get 

R2 


Sub- 


that  is,  the  capacity  of  a  condenser  is  different  with  different 
dielectrics  and,  as  has  already  been  shown,  varies  directly  with 
the  area  of  the  conducting  surfaces  and  inversely  as  their  distance 
apart. 


70  ELEMENTS  OF  ELECTRICITY. 

90.  Dielectric  Capacity.— The  fact  that  the  capacity  of  a  con- 
denser varies  with  the  medium  between  the  plates  may  be  shown 
by  a  simple  experiment.     If  the  air  condenser  (Fig.  38)  be  charged 
to  a  certain  potential  and  then,  without  altering  the  charge  or  the 
distance  apart  of  the  plates,  a  slab  of  paraffine  be  inserted  between 
them,  the  potential  will  immediately  drop.    If  mica  be  used  the 
drop  will  be  even  greater.     Since  the  potential  is  reduced  the 
condenser  will  require  a  greater  charge  to  bring  it  to  its  original 
potential,  that  is,  by  substituting  for  air  these  other  media  its 
capacity  is  increased. 

Since  without  changing  the  geometrical  arrangement  of  a  con- 
denser but  by  substituting  one  dielectric  for  another  we  alter  its 
capacity,  and  since  we  have  seen  that  the  charge  resides  on  this 
dielectric  and  not  on  the  conducting  plates,  we  naturally  associate 
the  idea  of  capacity  with  the  dielectric  itself  and  therefore  speak 
of  dielectric  capacity.  We  use  air  as  the  standard  of  comparison 
and  when  we  say  that  the  dielectric  capacity  of  mica  is  six  we  mean 
that  a  condenser  in  which  mica  is  the  dielectric  has  six  times  the 
capacity  of  one  with  air  as  the  dielectric  but  otherwise  precisely 
similar.  The  dielectric  capacity  of  a  substance  is  therefore  meas- 
ured by  the  ratio  of  the  capacity  of  a  condenser  in  which  the  sub- 
stance is  employed  as  the  dielectric  to  that  of  the  same  condenser 
in  which  air  has  been  substituted  for  the  substance.  This  ratio  is 
represented  by  k  in  the  last  expression  in  the  preceding  paragraph. 
This  factor  k  is  sometimes  called  the  dielectric  coefficient  since  it 
is  the  coefficient  by  which  the  capacity  of  an  air  condenser  must 
be  multiplied  to  obtain  the  capacity  of  the  same  condenser  in 
which  the  corresponding  dielectric  has  been  substituted  for  air. 
Reference  to  Par.  55  will  show  that  this  is  the  reciprocal  of  what 
was  there  called  the  "dielectric  coefficient  of  repulsion,"  whence 
it  follows  that  in  a  medium  whose  dielectric  coefficient  is  k,  the 
force  exerted  between  charged  bodies  is  |th  as  much  as  the  force 
exerted  between  these  bodies  in  air. 

91.  Determination  of  Dielectric  Capacity. — In  Faraday's  deter- 
mination  of   dielectric   capacity  he   used   spherical   condensers 
similar  to  the  one  represented  in  Fig.  40  but  with  the  opening  in 
the  outer  sphere  closed  by  an  insulating  stopper  through  which 
the  stem  of  the  inner  sphere  passed.    The  outer  sphere  was  sup- 
plied with  a  stop  cock  by  which  the  air  between  the  spheres  could 
be  drawn  off  and  liquids  or  gases  introduced,  also  the  outer  sphere 


STATIC  ELECTRICITY.  71 

could  be  separated  into  halves  when  it  became  necessary  in  in- 
serting or  removing  other  materials.  Two  of  these  condensers  of 
equal  size  were  taken.  In  one  air  was  retained  as  the  dielectric; 
into  the  other  was  introduced  the  substance  whose  dielectric 
capacity  was  to  be  determined.  Suppose  the  space  in  the  second 
one  to  be  filled  with  oil.  The  air  condenser  was  now  charged  to  a 
certain  potential  which  was  carefully  measured  by  the  torsion 
balance.  The  outer  coatings  of  the  two  condensers  were  next 
placed  in  contact,  either  directly  or  through  a  third  body,  and  were 
thus  brought  to  a  common  potential.  Finally,  the  inner  coatings 
were  brought  into  contact.  The  air  condenser,  being  at  a  higher 
potential,  gave  up  a  portion  of  its  charge  to  the  oil  condenser  until 
equality  of  potential  was  reached.  If  the  capacities  of  the  two 
condensers  were  equal,  the  charge  would  be  divided  equally 
between  them  and  the  resultant  potential  would  be  one-half  that 
of  the  original  potential.  If  the  capacity  of  the  oil  condenser  were 
greater  than  that  of  the  air  condenser,  the  oil  condenser  would  take 
more  than  half  the  charge  and  the  resultant  potential  would  be 
less  than  half  the  original  potential.  If  the  capacity  of  the  oil 
condenser  were  less  than  that  of  the  air  condenser,  the  resultant 
potential  would  be  greater  than  one-half  of  the  original.  In  either 
case,  the  resultant  potential  having  been  measured,  the  dielectric 
capacity  is  calculated  as  follows.  Let  Q  be  the  original  charge  of 
the  air  condenser,  V  its  original  potential,  V  the  potential  of  both 
condensers  after  division  of  the  charge,  K  their  capacity  when 
used  as  air  condensers  and  k  the  dielectric  capacity  of  the  oil. 
From  Par.  79  we  have 

K=Q,  whence Q  =  VK 

The  charge  in  the  air  condenser  after  contact  is 

Q'  =  V'K 
The  charge  in  the  oil  condenser  is 

Q"  =  k(V'K} 

The  sum  of  the  separate  charges  must  be  equal  to  the  original 

charge,  hence 

VK  =  V'K+k(V'K) 
whence 


72  ELEMENTS  OF  ELECTRICITY. 

92.  Dielectric  Capacity  of  Various  Substances. — The  dielectric 
capacity  of  many  insulating  materials  has  been  measured  and  some 
of  the  accepted  determinations  are  given  in  the  table  below. 
There  is  wide  variation  in  the  results  obtained  by  different  inves- 
tigators and  this  is  due  to  the  fact  that  the  capacity  of  a  condenser 
is  greater  if  the  charge  be  slowly  imparted  than  if  it  be  suddenly 
applied  and  as  suddenly  withdrawn.    In  the  first  case  the  medium 
yields  and  accommodates  itself  to  the  stress  put  upon  it.    By  the 
so-called,  instantaneous  method  of  determining  dielectric  capacity, 
the  condenser  is  charged  and  discharged  several  hundred  times  per 
second  and  the  determinations  are  less  than  those  obtained  by  the 
slow  methods.    The  dielectric  capacity  of  a  vacuum  is  about  .94; 
that  of  the  various  gases  differs  from  that  of  air  in  the  third  or 
fourth  decimal  place  only. 

Table  of  Dielectric  Capacities. 

Paper  1.5  Mica  4.0  to  8 

Beeswax  1.8  Porcelain  4.4 

Paraffine  2.0  to  2.3  Glycerine  16.5 

Petroleum  2.0  to  2.4  Ethyl  Alcohol  22.0 

Ebonite  2.0  to  3.2  Methyl  Alcohol  32.5 

Rubber  2.2  to  2.5  Formic  Acid  57.0 

Shellac  2.7  to  3.6  Water  80.0 

Glass  3.0  to  10.  Hydrocyanic  Acid  95.0 

93.  Dielectric  Strength.— The   quantity   of   electricity   which 
must  be  imparted  to  a  condenser  to  raise  its  potential  unity  de- 
pends upon  the  capacity  of  the  condenser.    If  the  plates  of  a  con- 
denser be  connected  to  two  objects  between  which  unit  difference 
of  potential  is  maintained,  the  condenser  will  receive  the  charge 
which  is  the  measure  of  its  capacity.    If  the  difference  of  potential 
between  the  two  objects  be  doubled,  the  condenser  will  receive  a 
charge  twice  as  great  and  so  on.    In  other  words,  as  has  been 
stated  in  Par.  79,  the  quantity  of  electricity  which  can  be  trans- 
ferred to  a  condenser  depends  upon  its  capacity  and  also  upon  the 
difference  of  potential  maintained  between  the  two  plates.    By 
increasing  this  difference  of  potential,  a  greater  and  greater  charge 
can  be  given  to  the  condenser  but  this  can  not  go  on  indefinitely 
for  as  the  potential  increases,  the  strain  upon  the  dielectric  in- 
creases until  finally  it  is  pierced  by  a  spark  and  the  condenser  is 
discharged.    The  resistance  which  a  medium  offers  to  piercing  by 


STATIC  ELECTRICITY.  73 

the  spark  is  called  its  dielectric  strength  and  is  measured  by  the 
maximum  difference  in  potential  in  volts  which  a  given  thickness 
(one  centimeter)  of  the  medium  will  stand  before  piercing  occurs. 
It  is  difficult  of  accurate  determination  since  it  is  affected  by 
temperature  and  pressure,  by  the  size  and  shape  of  the  bodies 
between  which  the  sparks  pass  and  by  the  manner  in  which  the 
electric  pressure  is  applied,  that  is  whether  constantly  in  one 
direction  or  alternately  in  opposite  directions. 

The  dielectric  strength  of  air  has  been  investigated  by  a  number 
of  observers.  A  minimum  difference  of  potential  of  300  volts  is 
required  to  produce  a  spark  at  all,  even  across  a  space  of  less  than 
.01  of  an  inch.  Sparks  pass  more  readily  between  points  than 
between  bodies  of  other  shapes.  The  strength  increases  with  the 
density  of  the  air,  whether  produced  by  falling  temperature  or  by 
increasing  barometric  pressure.  If  air  be  under  a  pressure  of  500 
pounds  per  square  inch,  it  can  be  hardly  pierced  at  all.  On  the 
other  hand,  a  vacuum  offers  an  equal  resistance.  To  throw  a 
spark  between  two  points  an  inch  apart  requires  about  20,000 
volts  and  to  produce  a  15-inch  spark  requires  145,000  volts.  To 
pierce  one  centimeter  of  paraffine  requires  130,000  volts,  one 
centimeter  of  ebonite  about  200,000  and  one  centimeter  of  mica 
about  350,000. 

94.  Commercial  Condensers. — Condensers  are  used,  as  will  be 
explained  later,  in  certain  electrical  measurements,  in  telegraphy 


HBB5SB93B 

Fig.  42. 

and  in  the  production  of  high  potential  electricity  by  means  of 
induction  coils.  They  are  usually  constructed  of  alternate  layers 
of  tin-foil  and  mica  or  of  tin-foil  and  waxed  paper  pressed  tightly 
together  and  thus  including  a  large  surface  in  very  small  bulk. 
The  alternate  sheets  of  foil  are  connected  as  shown  diagrammat- 
ically  in  Fig.  42  (in  which  the  shaded  spaces  represent  the  paper 


74  ELEMENTS  OF  ELECTRICITY. 

and  the  heavy  lines  the  foil)  and  the  whole  is  contained  in  a  rect- 
angular or  cylindrical  case  provided  with  the  proper  terminals. 
The  one  represented  in  the  figure  is  of  invariable  capacity  but  by 
connecting  the  sheets  of  foil  together  in  groups  attached  to  separate 
terminals  it  is  possible  to  use  at  will  different  fractions  of  the  entire 
condenser. 

95.  Practical  Unit  of  Capacity.  —  The  practical  unit  of  capacity, 
the  farad  ,  is  denned  as  the  capacity  of  that  body  whose  potential 
is  raised  one  volt  by  one  coulomb  of  electricity.  The  coulomb  will 
be  defined  later  (Par.  228)  but  we  have  already  seen  (Par.  56)  that 
it  is  three  billion  (3X109)  times  as  large  as  the  electrostatic  unit 
of  quantity.  We  have  also  seen  (Par.  77)  that  the  electrostatic 
unit  of  potential  is  equal  to  300  volts.  Since  one  electrostatic  unit 
of  quantity  raises  the  potential  of  a  sphere  of  one  centimeter  radius 
300  volts,  one  coulomb  would  raise  the  potential  of  such  a  sphere 
to  3X109X300,  or  nine  hundred  billion  (9X1011)  volts,  and  a 
sphere  of  9X1011  centimeters  radius  would  be  raised  one  volt  by 
one  coulomb  and  would  therefore  have  a  capacity  of  one  farad. 
The  radius  of  such  a  sphere  is  about  5,600,000  miles  or  about 
1,400  times  as  large  as  that  of  the  earth.  A  farad  is  therefore  so 
great  that  in  practice  one-millionth  of  a  farad  (or  a  micro-farad) 
is  used.  An  isolated  sphere  of  9xl05  centimeters  radius  (about 
5.6  miles)  would  have  a  capacity  of  one  micro-farad.  A  mica-tin- 
foil condenser  containing  about  25  square  feet  of  tin-foil,  has  also 
a  capacity  of  about  one  micro-farad. 

Since  a  sphere  of  9X105  centimeters  radius  has  a  capacity  of 
one  micro-farad,  a  sphere  of  one  centimeter  radius  (or  a  sphere 
of  unit  electrostatic  capacity)  has  a  capacity  of 

micr°-farad 


96.  Work  Expended  in  Charging  a  Condenser.  —  In  Par.  72  it 
was  shown  that  the  potential  at  a  point  was  measured  by  the  work 
done  in  bringing  up  to  that  point  from  an  infinite  distance,  or  from 
a  point  of  zero  potential,  a  unit  charge.  If  the  potential  be  V,  we 
mean  that  the  work  done  in  bringing  up  the  unit  charge  is  V  ergs. 
The  work  done  in  bringing  up  a  charge  Q  would  [therefore  be  QV 
ergs,  although  the  potential  of  the  point  would  still  remain  V,  that 
is,  the  assumption  is  that  the  charge  brought  up  does  not  increase 
the  potential  of  the  point.  The  potential  in  this  case  is  analogous 


STATIC  ELECTRICITY.  75 

to  the  head  of  a  body  of  water  which  body  is  of  such  extent  that 
its  level  is  not^appreciably  altered  by  the  pumping  up  of  additional 
quantities.  However,  the  case  is  different  if  the  charge  is  to  be 
brought  up  to  a  body  of  limited  capacity.  Suppose  we  have  a 
sphere  of  unit  capacity  and  at  zero  potential.  At  first  sight  it 
might  seem  that  to  transfer  to  this  sphere  from  zero  potential  a 
certain  charge  would  not  require  the  expenditure  of  any  energy. 
But  suppose  the  charge  to  be  brought  up  by  successive  portions. 
The  first  portion  could  be  brought  up  without  the  expenditure  of 
energy  but  would  raise  the  potential  of  the  sphere  and  would  repel 
the  second  portion  as  the  latter  approached.  These  two  portions 
would  repel  the  third  still  more  strongly  and  so  on,  the  work  re- 
quired to  bring  up  the  successive  portions  increasing  in  regular 
progression.  The  potential  in  this  second  case  is  analogous  to  the 
head  of  water  in  a  narrow  vessel,  each  portion  that  is  added  raising 
the  level  and  thus  increasing  the  work  which  must  be  expended  to 
bring  up  the  succeeding  portion. 

To  determine  the  amount  of  work  in  bringing  up  in  this  manner 
by  n  successive  portions  a  charge  Q.  The  first  portion  Q/n  would 
raise  the  potential  of  the  unit  sphere  to  Q/n.  To  bring  a  unit 
charge  to  a  point  of  such  potential  would,  from  the  definition  of 
potential,  require  an  expenditure  of  Q/n  ergs,  therefore  to  bring 
up  a  charge  of  Q/n  will  require  Q/n  times  as  much  or  Q2/n2  ergs. 
The  second  portion  would  therefore  require  an  expenditure  of 
Q2/n2  ergs  and  the  potential  would  become  2Q/n.  Similarly,  the 
third  portion  would  require  2Q2/n2  ergs  and  the  potential  would 
become  3Q/w  and  so  on.  To  bring  up  n  portions  would  require  a 
total  expenditure  of 

IS!  +*$+•<$!+  •  •  •  +«•-»©•- 


=  {1  +  2  +  3+     .     .     .     +(rc-l) 
The  sum  of  this  series  obtained  by  applying  the  formula 


in  which  a  is  the  first  term,  I  the  last,  and  n  the  number  of  terms 
(in  this  case  =n  —  1), 

13          ^•fergs=(i-9!ergs 


76  ELEMENTS  OF  ELECTRICITY. 

which  when  n  increases  indefinitely  becomes 

Q2 
^ergs 

and  the  corresponding  potential 

n 

which  last  also  follows  directly  from  the  fact  that  the  sphere  is  of 
unit?  capacity. 

Since  Q  =  V,  the  above  expression  for  the  work  may  be  written 

iQVergs 

that  is,  the  work  done  in  bringing  up  from  zero  potential  to  a  body 
of  limited  capacity,  likewise  at  zero  potential,  a  charge  Q  by  which 
the  potential  of  the  body  is  raised  to  V  is  just  one-half  the  work 
done  in  bringing  up  the  same  charge  from  a  point  of  zero  potential 
to  a  point  whose  potential  is  V. 

97.  Energy  of  a  Condenser. — If  the  body  to  which  the  charge  is 
brought  is  of  capacity  K  instead  of  unity,  the  expression  J  QV, 
since  Q  =  V  K,  may  be  put  in  the  form  J  Q2/  K,  that  is,  if  a  charge 
Q  be  given  to  a  condenser  of  capacity  K,  the  work  spent  is  propor- 
tional to  the  square  of  the  charge  and  inversely  proportional  to  the 
capacity  of  the  condenser. 

If  the  condenser  be  discharged  it  will  give  out  as  much  energy 
as  was  expended  in  charging  it  and  therefore  the  expression 
J  Q2/  K  also  represents  the  energy  of  discharge  or  the  energy  of 
the  condenser. 

If  for  Q  we  substitute  its  value  V  K,  the  expression  becomes 

\V^K 

that  is,  the  energy  of  a  condenser  varies  as  the  square  of  its 
potential  and  as  its  capacity.  This  principle  is  utilized  in  the 
quadrant  electrometer  to  be  described  later  (Par.  103). 


STATIC  ELECTRICITY.  77 


CHAPTER  11. 

ELECTROSTATIC   MEASUREMENTS. 

98.  Electrostatic  Measurements. — The  electrostatic  quantities 
which  we  most  frequently  desire  to  measure  are  quantity  of  charge 
and  difference  of  potential.    Of  these  two,  the  latter  is  the  more 
important  but  if  we  may  measure  either  one  we  may  determine 
the  other  indirectly.     Thus,  if  an  unknown  charge  raises  the 
potential  of  a  certain  conductor  by  a  given  amount,  we  have  only 
to  find  out  how  much  its  potential  is  raised  by  a  unit  charge  and 
can  then  determine  at  once  the  quantity  of  the  unknown  charge, 
or  similarly,  can  determine  the  potential  to  which  a  known  charge 
will  raise  a  given  conductor. 

99.  Unit    Jars. — At  first,   attempts   were   made   to   measure 
charges  directly  by  means  of  what  were  called  "unit  jars."    These 
were  small  Leyden  jars,  their  outer  coatings  connected  with  a 
knob  which  could  be  made  to  approach  or  recede  from  the  knob 
communicating  with  the  inner  lining.    By  adjusting  the  air  gap 
between  these  knobs  a  greater  or  a  lesser  charge  could  be  given 
to  the  jar  before  a  discharge  took  place.     They  were  used  to 
measure  the  charge  imparted  by  a  machine  to  a  large  Leyden  jar 
or  to  a  battery  of  these  jars.     One  was  inserted  between  the 
machine  and  the  knob  of  the  large  jar.    Obviously  no  charge  could 
pass  to  the  large  jar  until  the  unit  jar 

filled  up  and  discharged  and  the  amount 
was  determined  by  counting  the  num- 
ber of  sparks.  (  A 

100.  Principle    of    Electrometers.— 

Instruments  for  measuring  differences 
of  electrostatic  potential  are  called  elec- 
trometers. The  principle  upon  which 
they  operate  will  be  understood  from 
the  following.  Suppose  A  and  B  (Fig. 

43)  to  be  two  bodies  between  which  there  exists  a  difference  of 
electrostatic  potential  which  we  desire  to  measure.    For  one  reason 


78  ELEMENTS  OF  ELECTRICITY. 

or  another  it  is  generally  impracticable  to  measure  the  difference 
of  potential  between  the  bodies  themselves  and  we  therefore  have 
to  transfer  the  potentials  to  the  parts  of  our  instrument.  Let  C  and 
D  be  two  small  spheres,  D  fixed  and  C  attached  to  a  spring  which 
can  be  extended  or  compressed  and  which  has  a  scale  from  which  the 
force  producing  the  extension  or  the  compression  can  be  read.  If 
A  and  C  be  connected  by  a  wire  they  will  at  once  attain  the  same 
potential  and  the  charge  imparted  to  C  will  vary  directly  with  the 
potential  of  A.  Likewise  if  B  be  connected  with  D,  D  will  attain 
the  potential  of  B  and  acquire  a  charge  proportional  to  this 
potential.  C  and  D  will  now  attract  or  repel  each  other  with  a 
ibrce  which  can  be  read  from  the  scale  and  which  is  proportional 
to  the  product  of  the  charges  which  in  turn  are  proportional  to 
the  potentials.  But  C  and  D  are  of  the  same  potentials  as  A  and 
B,  respectively,  and  therefore  this  force  is  proportional  to  some 
function  of  the  difference  of  potential  between  A  and  B.  If 
A  or  B  be  very  small,  they  would  part  with  a  considerable  portion 
of  their  charge  when  connected  to  C  and  D  and  the  resultant 
potential  would  be  less  than  the  original  potential,  but  usually 
A  and  B  are  so  large  that  the  small  loss  of  potential  can  be  neg- 
lected. For  example,  B  is  frequently  the  earth,  in  which  case  D 
is  of  zero  potential. 

Coulomb's  torsion  balance,  already  described,  may  be  used  as 
an  electrometer,  the  removable  ball  being  touched  to  the  body 
whose  potential  is  required  and  thus  obtaining  a  charge  propor- 
tional to  that  potential,  but  the  usual  form  of  electrometers  use 
plates  or  flat  moving  parts  instead  of  the  spheres  described  above. 

101.  The  Attracted  Disc  Electrometer.— The  attracted  disc 
electrometer  was  invented  by  Snow  Harris  but  perfected  by  Lord 
Kelvin.  Its  essential  parts  are  shown  diagrammatically  in  Fig.  44. 
AB  is  a  lever  pivoted  upon  a  tightly  stretched  horizontal  wire  CD. 
At  one  end  is  a  counterpoise  B,  at  the  other  end  a  fork  A  which 
embraces  an  upright  E  and  across  which  there  is  stretched  a  fine 
hair.  From  the  fork  there  is  suspended  so  as  to  hang  horizontally 
a  circular  disc  G  which  moves  with  a  minimum  clearance  inside  of 
a  fixed  ring  R.  A  portion  of  this  ring  is  represented  in  the  diagram 
as  cut  away.  Below  the  disc  and  ring  is  a  circular  plate  P  insu- 
lated by  being  mounted  upon  a  glass  stem  which  in  turn  is  attached 
to  a  brass  support.  The  plate  P  can  be  raised  or  lowered  by  turn- 
ing the  micrometer  screw  H,  which  is  so  arranged  that  the  plate 


STATIC  ELECTRICITY.  79 

is  always  kept  strictly  parallel  to  the  disc  G  and  which  permits  the 
distance  through  which  P  has  been  moved  to  be  read  with  great 
accuracy.  Upon  the  upright  E  there  are  two  black  dots  and  when 
the  lower  surface  of  G  is  exactly  in  the  plane  of  the  lower  surface 


Fig.  44. 

of  R  the  hair  at  A  is  just  between  these  dots.  There  is  a  lens  L 
by  which  the  position  of  the  hair  is  observed  and  it  is  said  that  an 
error  of  as  little  as  1/50,000  of  an  inch  can  be  detected  and  cor- 
rected. G  and  R  are  connected  electrically  by  means  of  a  wire  from 
R  to  D.  By  moving  the  counterpoise  B  or  by  twisting  the  wire 
CD,  the  disc  G  is  given  an  initial  position  slightly  above  the  ring 
R.  Small  weights  are  then  placed  upon  G  until  the  lower  surfaces 
of  G  and  R  lie  in  a  common  plane.  From  the  weights  used  the 
force  in  dynes  to  effect  this  is  determined.  The  weights  are  then 
removed.  If  now  a  charge  be  given  to  G  it  will  induce  an  opposite 
charge  in  P,  G  and  P  will  attract  each  other  and  G  will  be  drawn 
downward.  By  varying  the  position  of  P  the  downward  pull  on 
G  can  be  so  adjusted  that  the  plane  of  the  lower  surface  of  G  coin- 
cides with  that  of  the  lower  surface  of  R.  At  this  point,  the  force 
of  attraction  equals  the  force  in  dynes  as  determined  by  the  weights. 

102.  Theory  of  Attracted  Disc  Electrometer. — In  Par.  40  we 

saw  that  a  charge  imparted  to  a  flat  disc  was  uniformly  distributed 
over  the  central  portion  but  much  denser  around  the  edges.  When 
G  and  R  are  in  one  plane  they  practically  constitute  one  surface. 
The  surface  density  over  the  movable  disc  G  is  therefore  quite 
uniform  and  the  excessive  density  is  confined  to  the  fixed  ring  R 
which  on  this  account  was  called  by  Lord  Kelvin  the  "guard  ring." 


80  ELEMENTS  OF  ELECTRICITY. 

To  measure  the  difference  in  potential  between  two  bodies,  R 
(and  hence  G)  is  connected  to  one  and  P  to  the  other.  Let  V  be 
the  potential  of  P  and  V"  that  of  G.  The  surface  density  of  G 
is  6  and  that  of  the  induced  charge  upon  P  is  -  5.  The  difference 
of  potential,  V'-V",  is  measured  (Par.  72)  by  the  amount  of 
work  done  in  moving  a  unit  positive  charge  from  P  to  G,  a  dis- 
tance D.  The  force  exerted  upon  a  unit  charge  placed  between 
P  and  G  is  (Par.  66)  an  attraction  of  2  wd  by  one  and  a  repulsion 
of  2  7J-5  by  the  other,  or  a  total  force  of  4  nd.  The  work  therefore  is 

V'-V"  =47r5D 

Again,  every  unit  charge  upon  G  is  attracted  by  P  with  a  force 
of  2  7r6  dynes.  If  S  be  the  area  of  G,'  the  charge  upon  G  is  Sd  and 
the  total  force  of  attraction  is 

F  =  2wdzS 

Whence  /   p 

8 


Substituting  in  the  expression  for  V  —  V",  we  have 

V-  V"  =  D\/^jr- 

F  is  determined  in  dynes  from  the  weights  as  described  above, 
D  is  in  centimeters,  S  is  in  square  centimeters  and  V  —  V",  the 
difference  in  potential,  is  in  absolute  electrostatic  units.  As 
explained  in  Par.  77,  if  this  be  multiplied  by  300  it  is  converted 
into  volts. 

Since  S  is  constant  and  F  may  be  kept  constant,  the  expression 

SirF 

is  a  constant  and  can  be  determined  once  for  all.     The 

difference  of  potential  between  G  and  P  is  therefore  directly  pro- 
portional to  the  distance  between  the  plates  when  the  instrument 
is  balanced. 

The  actual  distance  between  the  plates  is  difficult  of  measure- 
ment. If  P  be  connected  to  some  other  charged  body  whose 
potential  is  V"  and  the  apparatus  be  balanced  we  have 

V"-  v  =  iXV^fr 

*       o 

Subtracting  this  from  the  expression  above  we  have 


STATIC  ELECTRICITY. 


81 


that  is,  the  difference  of  potential  between  two  charged  bodies, 
each  being  compared  to  a  third,  is  proportional  to  the  difference 
in  the  distance  between  the  plates  in  the  two  observations  and 
this  difference  in  distance  is  easily  and  accurately  determined  from 
the  micrometer  screw. 

By  using  the  earth  as  the  third  body,  that  is,  by  connecting  G 
to  the  earth,  V"  in  the  above  becomes  zero. 

There  are  many  refinements  used  in  connection  with  this  instru- 
ment but  it  is  not  necessary  to  describe  them  here. 

103.  The  Quadrant  Electrometer. — The  quadrant  electrom- 
eter of  Lord  Kelvin  is  a  more  sensitive  instrument  than  the 


Fig.  45. 

foregoing.  It  is  shown  diagrammatically  in  Fig.  45.  A  flat 
cylindrical  brass  box  is  cut  into  quadrants  A,  B,  C  and  D  (this 
last  is  represented  as  cut  away  to  show  the  interior)  which  are 
fastened  to  the  top  of  the  apparatus  (not  shown)  by  the  glass 
pillars  E,  F,  etc.  The  diametrically  opposite  quadrants  A-C  and 


82  ELEMENTS  OF  ELECTRICITY. 

B-D  are  connected  by  wires  (Fig.  46).  Within  the  box  is  a  flat 
needle  N  of  light  aluminum  plate  which  is  fastened  rigidly  to  an 
aluminum  wire  extending  above  and  below.  The  needle  is  sus- 
pended by  one  or  by  two  fibres  of  silk  or  by  a  single  fibre  of  quartz 
L  attached  to  the  upper  end  of  this  wire.  To  the  lower  end  of  the 
wire  there  is  fastened  a  platinum  wire  which  dips  into  some  sul- 
phuric acid  in  a  glass  jar:  This  jar,  which  also  serves  as  a  case  for 
the  lower  part  of  the  instrument,  has  an  outer  coating  of  tin-foil 
and  with  the  sulphuric  acid  within  is  thus  a  Leyden  jar.  The 
acid  also  keeps  the  air  in  the  jar  dry  and  prevents  loss  of  charge  by 
moisture.  The  needle  swings  midway  between  the  top  and  bottom 
of  the  box  and  symmetrically  over  the  separation  between  the 
quadrants.  Upon  the  wire  above  the  needle  there  is  fastened  a 
small  circular  concave  mirror  M.  The  angle  through  which  the 
needle  turns  is  determined  either  by  the  reflection  of  a  beam  of 
light  from  this  mirror  upon  a  scale  or  by  observing  in  the  mirror 
by  means  of  a  telescope  the  reflection  of  a  printed  scale  fastened 
just  above  the  telescope.  These  methods  of  determining  the  angle 
of  deflection  are  described  in  detail  later  on;  the  former  in  connec- 
tion with  the  mirror  galvanometer  (Par.  377),  the  latter  in  con- 
nection with  the  suspended  coil  galvanometer  (Par.  378).  There 
project  from  the  glass  case  terminals,  called  "electrodes,"  one  of 
which  connects  with  each  pair  of  quadrants  and  one  with  the  acid 
of  the  jar. 

To  use  the  instrument,  one  pair  of  quadrants  is  connected  to 
one  body,  the  other  pair  to  the  second  body  between  which  the 
difference  of  potential  is  to  be  measured.  The  quadrants  thus 
acquire  the  potentials  of  the  respective  bodies. 
The  Leyden  jar  is  then  charged  until  the  needle 
has  a  high  potential  V3  which  by  certain  arrange- 
ments, not  necessary  to  describe  here,  is  kept 
constant  during  the  measurement.  If  the 
charges  are  of  the  same  kind,  mutual  repulsion 
Fi  46  exists  between  the  charge  on  the  needle  and 

those  on  the  adjacent  quadrants  and  the  needle 
moves  toward  the  quadrant  of  lesser  charge,  that  is,  of  lower  po- 
tential. The  deflection  of  the  needle  is  read  from  the  mirror  and 
the  difference  of  potential  is  proportional  to  this  deflection. 

This  instrument  is  sufficiently  delicate  to  measure  differences 
of  potential  almost  as  small  as  .01  of  a  volt. 


STATIC  ELECTRICITY.  83 

104.  Theory  of  the  Quadrant  Electrometer.—  Figure  47  repre- 
sents a  cross-section  of  the  needle  and  two  adjacent  quadrants, 
the  potentials  being  as  marked  and  y3  being  much  greater  than 
either  of  the  others.  V\  Y3 
constitute  a  condenser,  V2  V3 
another.  The  energy  of  a  con- 
denser (Par.  97)  is  %V2K  in 
which  V  is  the  difference  in 
potential  between  the  two  Fis-  47> 

plates  and  K  is  its  capacity.    The  energy  of  Vi  V3  is  thereiore 

and  that  of  y2  Vs  is 

y3  being  symmetrically  suspended  with  respect  to  V\  and  V2  as 
it  swings  to  the  right  or  left  it  increases  the  surface  embraced  by 
one  by  exactly  the  same  amount  as  it  decreases  the  surface  em- 
braced by  the  other  and  as  its  edges  still  remain  well  inside  of 
Vi  and  y2  it  increases  the  capacity  of  one  condenser  and  decreases 
by  an  equal  amount  that  of  the  other.  Let  this  increment  of 
capacity  for  a  unit  angular  motion  of  Y3  be  denoted  by  k;  the 
decrement  will  be  —A:.  The  change  in  the  energy  of  Vi  V3  for  an 
angular  movement  6  will  therefore  be  JA0(V3  —  Vi)2  and  that 
of  V2  V3  will  be  -  %ke  (Y3  -V2)2.  The  total  change  in  the 
energy  of  the  system  will  be 


The  force  moving  the  needle  =  =  is  therefore 

pat 


F= 

or  the  force  between  the  needle  and  each  quadrant  is  proportional 
to  the  square  of  the  difference  of  potential  between  the  needle  and 
the  respective  quadrant. 

Simplifying  the  foregoing  expression  we  have 


or  the  force  tending  to  turn  the  needle  is  proportional  to  the 
difference  of  potential  between  the  quadrants  and  also  to  the 
difference  between  the  potential  of  the  needle  and  the  average  of 
the  potentials  of  the  two  quadrants. 


84  ELEMENTS  OF  ELECTRICITY. 

Since  V3  is  kept  constant  and  is  very  large  as  compared  to  Vi 
and  V2,  [  Vi  -  *  1" — ?J  may  be  taken  as  a  constant  and  the  ex- 
pression for  the  force  becomes 

F  =  a(Vi-V2) 

The  force  being  counterbalanced  by  the  torsion  of  the  sus- 
pending fibre,  the  difference  of  potential,  Vi  —  V2,  between  the 
two  bodies  being  examined  is  proportional  to  the  deflection  as 
indicated  by  the  mirror.  By  using  a  known  difference  of  potential 
the  constant  a  may  be  determined  once  for  all. 


MAGNETISM.  85 


PART  II. 
MAGNETISM. 


CHAPTER  12. 

MAGNETS. 

105.  Natural  Magnets. — Of  the  four  important  ores  of  iron  the 
richest  is  that  one  whose  chemical  formula  is  Fe304.    This  when 
pure  is  a  heavy  black  mineral,  often  coarsely  crystalline  but  also 
frequently  massive.    It  occurs  in  beds  in  many  widely  scattered 
localities  and  from  it  a  large  part  of  the  iron  and  steel  of  commerce 
is  made.     Some  specimens  of  this  ore  possess  the  remarkable 
property  of  attracting  and  picking  up  small  particles  of  iron  and 
steel.    If  such  a  specimen  be  dipped  or  rolled  in  iron  filings,  the 
filings  will  adhere  to  it  like  a  mossy  growth.    This  property  has 
been  known  for  nearly  3,000  years  and  because  the  best  speci- 
mens came  from  the  vicinity  of  the  town  of  Magnesia  in  Lydia 
they  were  called  by  the  Greeks  magnetis  lithos  (Magnesian  or 
Magnetian  stone),  whence  are  derived  our  name  magnet  and  the 
mineralogical  term  magnetite  or  magnetic  iron  ore.    To  distinguish 
these  magnets  from  those  prepared  artificially  they  are  usually 
called  native  or  natural  magnets. 

106.  Lodestones. — About  800  years  ago  an  additional  property 
of  magnets,  equally  as  remarkable  as  the  first,  became  known  to 
European  nations.    If  an  oblong  or  elongated  magnet  be  arranged 
so  that  it  is  free  to  rotate  in  a  horizontal  plane  (as  for  example  by 
suspending  it  by  a  thread  or  by  placing  it  upon  a  floating  cork  or 
by  balancing  it  upon  a  pivot)  it  will  take  up  a  north  and  south 
position,  the  same  end  always  returning  to  the  north,  no  matter 
what  may  be  its  primary  position.    This  property  was  quickly 
utilized  in  navigation  and  since  these  magnets  thus  led  the 
mariner  about  over  the  seas,  they  were  called  lodestones  (leading 
stones). 


86  ELEMENTS  OF  ELECTRICITY. 

107.  Fables  of  the  Ancients. — In  contemplating  the  mystical 
power  of  attraction  of  magnets,  the  ancients  gave  free  rein  to  their 
imagination  and  gravely  recorded  and  copied  from  each  other's 
writings  the  most  wonderful  statements  about  magnets.     They 
were  by  some  reputed  to  be  endowed  with  life  and  to  possess  a 
soul.    A  magnet  was  supposed  to  protect  from  witchcraft.     If 
held  in  the  hand  it  cured  cramps.    The  power  of  a  weakening 
magnet  could  be  restored  by  soaking  it  in  the  blood  of  a  buck 
while  if  it  were  rubbed  with  garlic  it  lost  its  power.    It  also  lost 
its  power  when  in  the  presence  of  a  diamond.    If  pickled  in  salt 
with  a  certain  fish,  the  remora  or  sucking  fish,  it  acquired  the 
property  of  attracting  gold  and  silver  and  could  thus  be  used  to 
fish  up  treasure  from  the  deepest  wells.    At  various  points  in  the 
Eastern  Seas  were  islands  of  lodestone  so  powerful  that  they  pulled 
the  nails  from  the  sides  of  vessels  and  thus  caused  their  loss.    In 
those  parts  ships  had  to  be  built  with  wooden  pegs.     In  India 
there  were  side  by  side  two  mountains,  one  of  lodestone  so  power- 
ful that  if  a  person  with  iron  nails  in  his  shoes  stepped  upon  it  he 
could  not  raise  his  feet  to  take  a  second  step,  the  other  of  a  sub- 
stance which  repelled  iron  so  strongly  that  such  a  person  found  it 
impossible  to  place  his  foot  upon  the  surface.    We  can  not  now 
understand  the  state  of  mind  of  these  writers,  for  very  simple 
experiments  would  have  readily  shown  the  absurdity  of  their 
statements. 

108.  Doctor  Gilbert.— Such  for  near  2,000  years  remained  the 
state  of  knowledge  until,  as  has  already  been  stated  (Par.  12),  a 
certain  Doctor  Gilbert  in  the  reign  of  Queen  Elizabeth  undertook 
a  series  of  investigations  of  the  properties  of  the  lodestone.    In 
1600  he  published  his  work,  De  Magnete  Magneticisque  Corporibus 
(On  the  Magnet  and  Magnetic  Bodies),  in  which  he  described  his 
experiments,  wonderful  for  their  simplicity  and  in  some  directions 
well  nigh  exhaustive.     Anticipating  the  Baconian  system,   he 
accepted  no  statements  about  magnets  until  he  had  confirmed 
these  statements  by  his  own  experiments  and  he  was  thus  able 
not  only  to  sweep  aside  the  mythological  rubbish  which  until  then 
passed  current  but  also  to  bring  forward  many  facts,  hitherto 
unknown.     In  short,  by  his  researches  he  brought  to  light  the 
majority  of  the  truths  and  principles  upon  which  our  present 
knowledge  of  magnetism  is  based. 


MAGNETISM. 


87 


109.  Artificial  Magnets. — If  a  bar  of  iron  or  of  steel  be  rubbed 
or  stroked  in  a  certain  manner  (see  Par.  162)  by  a  lodestone,  the 
bar  acquires  magnetic  properties.    Steel  is  found  to  be  more  reten- 
tive of  magnetism  than  iron  and  is  accordingly  used.     The  bar 
thus  magnetized  may  in  turn  be  used  to  produce  magnetism  in 
others.    There  is  another  and  better  method,  in  which  an  electric 
current  is  used  to  produce  magnets,  but  an  explanation  of  this 
method  must  be  deferred  until  later  (Par.  164).    These  artificial 
magnets,  on  account  of  their  strength,  of  the  ease  with  which  they 
may  be  prepared  and  of   the 

readiness  with  which  they  may 
be  given  any  desired  shape, 
have  quite  displaced  lodestones 
and  are  the  ones  referred  to  in 
the  following  pages.  The  com- 
monest forms  are  bars  and  the 

so-called   needles.     These   last  ^^^^       Fig.  48. 

are  usually  thin,  elongated,  losenge-shaped  magnets  with  a  socket 
at  the  center  by  which  they  may  be  pivoted  upon  a  sharp  point 
(Fig.  48).  In  the  best  needles  the  socket  is  jewelled. 

110.  Magnetic  Poles. — In  pursuing  a  certain  line  of  investi- 
gation, Gilbert  caused  to  be  cut  from  a  lodestone  a  regular  sphere 
to  which  he  applied  the  name  terrella  (little  globe).     When  this 
terrella  was  rolled  in  iron  filings  they  adhered  to  it  in  tufts,  not 
however  uniformly  over  its  surface  but  upon  two  restricted  areas 
at  the  opposite  ends  of  a  diameter.    These  regions  he  designated 
as  the  poles  of  the  terrella. 

If  a  bar  magnet  or  a  magnetic  needle  be  dipped  in  filings,  they 
will  adhere  only  to  the  regions  at  the  ends,  and  these  regions  are 

likewise  called  poles. 

If  such  a  magnet  be  balanced 
upon  a  cork  which  in  turn  floats 
in  a  vessel  of  water  (Fig.  49) 
it  will  oscillate  in  a  horizontal 
plane  and  finally  come  to  rest 
in  a  north  and  south  position. 
The  same  end  of  the  magnet 

Fig.  49.  always    points    north   and    is 

therefore  called  the  north  pole,  the  other  end  being  called  the 
south  pole.  The  fact  that  this  one  end  always  points  north  shows 


88  ELEMENTS  OF  ELECTRICITY. 

that  it  must  differ  from  the  other,  but  so  far  as  the  attraction 
of  iron  filings  and  the  lifting  of  iron  weights  is  concerned,  the  two 
ends  are  of  identical  properties.  The  north  and  the  south  poles 
are  frequently  designated  positive  and  negative,  respectively. 

111.  The  Poles  Inseparable. — Should  a  slender  bar  magnet 
(Fig.  50)  be  broken  in  half,  it  will  be  found  that  each  half  is  a 
complete  magnet  and  has  a  north  and  a  south  pole  nearly  as 

s  N 


N 


Fig.  50. 

strong  as  those  of  the  original  magnet.  If  one  of  these  halves  be 
again  broken,  the  fragments  will  each  have  a  north  and  a  south 
pole  and  so  on.  In  other  words,  it  is  impossible  to  get  a  separate 
north  or  south  pole  unaccompanied  by  an  equal  pole  of  the  oppo- 
site kind.  Explanation  of  this  fact  will  be  given  later  (Par.  152). 

112.  Magnetic  Attraction.— If  a  bar  magnet  be  dipped  into 
iron  or  steel  filings  and  then  be  lifted,  the  filings  will  be  found  to 


Fig.  51. 


cling  to  it  like  a  thick  mossy  growth  (Fig.  51).  Upon  examination 
the  following  peculiarities  will  be  noted. 

1st.  As  already  stated,  the  filings  do  not  adhere  all  over  but 
mainly  in  the  region  of  the  poles  and  none  at  all  in  the  central 
portion  of  the  magnet. 

2nd.  The  individual  filings  cling  to  the  magnet  by  their  ends 
rather  than  by  their  sides  and  at  each  pole  radiate  from  an  internal 
focus  near  the  end  of  the  magnet. 

3rd.  The  filings  cluster  more  thickly  along  the  edges  and  corners 
of  the  magnet  than  along  the  flat  surfaces. 


MAGNETISM. 


89 


4th.  Where  the  filings  are  thickest,  it  will  be  found  that  those 
which  cling  to  the  magnet  may  have  others  clinging  to  them  in 
turn,  and  these  may  have  still  others,  forming,  as  it  were,  chains. 

113.  The  Attraction  Takes  Place  Through  Intervening  Bodies. 

— The  magnetic  attraction  takes  place  at  a  distance  and  through 
space,  although  it  falls  off  rapidly  as  the  distance  increases.  Fine 
filings  will  leap  up  to  reach  a  strong  magnet  held  above  them. 
Furthermore,  the  attraction  is  propagated  through  intervening 
objects.  A  bar  magnet  inserted  in  a  glass  tube  will  attract  filings 
through  the  glass.  If  filings  be  sprinkled  upon  a  thin  board  or  a 
slate  or  a  sheet  of  glass  or  of  brass,  a  magnet  moved  about  beneath 
will  drag  after  it  the  filings  on  top.  There  is  but  one  screen  for 
the  magnetic  force  and  that,  as  will  be  explained  later  (Par.  143), 
is  a  comparatively  thick  plate  of  iron  or  steel. 

114.  The  Attraction  Mutual. — If  a  small  iron  bar  be  floated 
upon  a  cork  in  a  basin  of  water,  the  bar  and  cork  will  move  about 
in  pursuit  of  a  magnet  held  near.    If  the  bar  and  the  magnet  be 
made  to  change  places,  the  magnet  will  follow  about  after  the  iron 
bar. 

115.  Action  of  Magnets  upon  Each  Other. — The  mutual  action 
of  magnets  is  most  easily  studied  by  means  of  a  magnetic  needle. 
If  when  the  needle  has  come  to  rest,  its  north  end  be  approached 


Fig.  52. 

by  the  north  end  of  a  bar  magnet  (Fig.  52),  it  will  be  repelled  and 
move  off.  On  the  other  hand,  its  south  end  will  be  attracted  by 
the  north  end  of  the  magnet.  If  the  bar  magnet  be  turned  end 
for  end  and  its  south  end  be  held  to  the  north  end  of  the  needle, 
the  latter  will  be  attracted,  and  if  it  be  held  to  the  south  end,  this 
end  will  be  repelled.  We  see  then  that  magnetic  poles  follow  a  law 


90 


ELEMENTS  OF  ELECTRICITY. 


similar  to  that  given  for  positive  and  negative  charges  of  elec- 
tricity (Par.  24),  that  is,  like  poles  repel  and  unlike  poles  attract 
each  other. 

If  two  bars  of  similar  shape  and  size  attract  each  other  we 
would  know  that  one  of  them  was  a  magnet  but  without  other 
test  could  not  tell  which.  If  they  repelled  each  other  we  would 
know  that  they  were  both  magnets. 

116.  Why  a  Magnetic  Needle  Points  North  and  South.— Sup- 
pose that  upon  a  bar  magnet  resting  on  a  horizontal  surface  there 

be  placed,  as  shown  in  Fig. 
53,  a  magnetic  needle.  The 
north  pole  of  the  magnet 
will  repel  the  north  pole  of 
the  needle  but  will  attract 
its  south  pole;  the  south  pole 


Fig.  53. 


of  the  magnet  will  repel  the 


south  pole  of  the  needle  and  attract  its  north  pole.  The  needle 
will  in  consequence  take  up  a  position  parallel  to  the  axis  of  the 
bar  magnet  but  with  its  poles  in  reverse  direction.  Similar  experi- 
ments led  Gilbert  to  the  discovery  that  the  earth  itself  is  an  immense 
magnet,  its  poles  being  in  the  neighborhood  of,  but  not  coinciding 
exactly  with,  the  geographical  poles.  A  magnetic  needle  will 
therefore  take  up  a  position  approximately  in  the  plane  of  the 
earth's  magnetic  axis  for  the  same  reason  that  the  needle  in 
the  above  experiment  poised  parallel  to  the  axis  of  the  bar 
magnet. 

117.  The  Poles  Misnamed.— Gilbert  called  attention  to  a  fact 
following  directly  from  his  discovery,  that  is,  that  the  pole  of  the 
needle  which  is  attracted  by  the  earth's  north  magnetic  pole  (and 
which  we  have  called  its  north  pole)  should  strictly  be  called  its 
south  pole.    Subsequent  writers  in  view  of  this  have  sought  to 
avoid  confusion  by  using  the  terms  "north-seeking  pole"  and 
"south-seeking  pole,"  but  it  is  thought  that  the  shorter  expres- 
sions are  sufficiently  sanctioned  by  custom  and  that  no  ambiguity 
will  arise  if  in  the  following  pages  the  pole  of  the  needle  which 
points  north  be  designated  its  north  pole,  the  other,  its  south 
pole. 

118.  Magnetization  by  Induction.— A  soft  iron  nail  touched 
to  a  bar  magnet  will  cling  to  it.    If  a  second  nail  be  now  touched, 


MAGNETISM. 


91 


not  to  the  magnet  but  to  the  first  nail  (Fig.  54),  it  will  cling  to  this 
nail  and  even  a  third  nail  may  be  attached  to  the  second  and  so  on. 
If  while  thus  dangling  the  several 
nails  be  tested,  each  will  be  found 
to  possess  polarity,  the  upper  ends 
being  of  opposite  polarity  to  that 
end  of  the  magnet  to  which  they 
are  clinging,  the  lower  ends  being 
of  the  same  polarity.  If  the  mag- 
net be  removed  the  chain  of  nails 
will  fall  apart.  The  magnet  there-  Fig-  54- 

fore  influences  the  nails  so  that  for  the  time  being  they  them- 
selves are  magnets.  This  is  the  explanation  of  the  chains  of  filings 
referred  to  in  Par.  112.  The  phenomenon  is  called  magnetization 
by  induction. 

119.  Induction  Takes  Place  Through  Space. — Actual  contact 
is  not  necessary  for  induction.  A  piece  of  iron  or  steel  placed 
anywhere  in  the  vicinity  of  a  magnet  becomes  temporarily  a 
magnet.  This  fact  is  clearly  shown  by  the  following  experiment. 
A  soft  iron  bar  AB  (Fig.  55)  free  from  magnetism  is  arranged 


Fig.  55. 

upon  a  convenient  support.  Near  the  end  B  but  not  so  near  as 
to  be  attracted  into  contact  is  placed  a  needle.  If  the  north 
pole  N  of  a  bar  magnet  be  approached  to  the  end  A  of  the  iron 
bar,  but  not  actually  touching  the  same,  the  north  pole  of  the 
needle  will  be  repelled  from  B.  The  bar  A  B  becomes  a  magnet 
by  induction,  the  end  B  becoming  the  north  pole  and  repelling 
the  north  pole  of  the  needle.  To  show  that  the  repulsion  of  the 
needle  is  not  due  to  the  direct  action  of  the  bar  magnet,  if  A  B  be 
removed  the  effect  of  the  bar  magnet  upon  the  needle  is  almost 
negligible. 


92  ELEMENTS  OF  ELECTRICITY. 

120.  Magnetic  Attraction  Explained. — The  foregoing  enables 
us  to  explain  magnetic  attraction.    A  piece  of  iron  or  steel  near  a 
magnet  becomes  a  magnet  by  induction.    The  near  end  of  the 
piece  is  of  opposite  polarity  and  hence  attracted;  the  farther  end 
is  repelled  but  the  attraction  is  stronger  than  the  repulsion  (mag- 
netic attraction  and  repulsion  will  shortly  be  shown  to  follow  the 
law  of  inverse  squares)  and  the  piece,  if  free  to  do  so,  will  move 
bodily  up  to  the  magnet.    As  in  the  case  of  electric  charges,  in- 
duction precedes  attraction. 

121.  Other  Magnetic  Substances. — We  have  heretofore  men- 
tioned only  iron,  steel  and  the  lodestone  as  being  magnetic  sub- 
stances.    Two  other  metals,  nickel  and  cobalt,  are  noticeably 
magnetic,  though  much  less  so  than  the  above  mentioned,  and  many 
substances  are  feebly  so,  so  feebly  however  that  the  property  can 
be  detected  only  by  the  most  delicate  apparatus  and  for  practical 
purposes  may  be  neglected.    Among  these  substances  are  some  of 
the  salts  of  iron,  and  oxygen,  especially  when  liquefied. 

Gilbert  carefully  distinguished  between  magnets  and  magnetic 
substances.  A  magnet  exerts  its  attraction  at  certain  portions 
only,  has  polarity  and  its  poles  will  repel  similar  poles  of  a  second 
magnet.  A  magnetic  substance,  such  as  soft  iron,  has  no  polarity, 
attracts  either  pole  of  a  magnet  at  any  portion  of  its  surface  and 
does  not  attract  other  magnetic  substances. 

122.  Diamagnetism.— It  has  long  been  known  that  some  sub- 
stances, notably  bismuth  and  antimony,  are  repelled  from  the 
poles  of  a  magnet,  the  bodies  placing  themselves  so  that  their 
longer  axis  is  at  right  angles  to  the  magnet.    Explanation  of  this 
phenomenon  can  not  be  given  until  the  subject  of  electro-magnetics 
is  reached  (Par.  402).    The  repulsion  is  very  feeble  and  delicate 
instruments  are  required  to  detect  it.    Faraday  investigated  the 
magnetic  properties  of  many  bodies  and  those  which  are  attracted 
he  called  paramagnetics;  those  which  are  repelled,  diamagnetics. 
The  majority  of  liquids,  except  those  containing  in  solution  the 
salts  of  iron,  are  feebly  diamagnetic.    The  subject  is  of  theoretical 
interest  only. 


MAGNETISM. 


93 


CHAPTER  13. 

MEASUREMENT   OF  MAGNETIC  FORCES. 

123.  Coulomb's  First  Law. — The  first  law  of  magnetic  force 
has  already  been  given  (Par.  115)  and  is  that  like  poles  repel  and 
unlike  poles  attract  one  another.    The  second  law  deals  with  the 
variation  of  this  force  of  attraction  or  repulsion.    Before  develop- 
ing it,  we  must  get  some  preliminary  notion  of  what  is  meant  by 
the  strength  of  magnets. 

124.  Lifting  Power  of  Magnets. — At  first  sight  it  might  seem 
that  a  simple  way  to  determine  and  compare  the  strength  of  mag- 
nets would  be  to  ascertain  the  weight  which  they  could  support. 
Various  pieces  of  apparatus  have  been  devised  for  this  purpose. 
For  example  (Fig.  56)  the  magnet  is  held  vertically  in  a  frame 
and  supports  by  its  attraction  an  iron  piece  or  armature  A. 
Attached  to  this  armature  is  a  hook  from 

which  hangs  a  receptacle  into  which  fine 
sand  is  slowly  poured.   When  the  accumu- 
lated weight  reaches  a  certain  point  the 
armature  is  torn  away  and  with  the  recep- 
tacle drops  to  a  table  placed  just  beneath 
to  receive  it.    The  total  weight  supported  N\        \ 
by   the   magnet  is  then  determined   by  \\\ 
weighing.  \\ 

When,  however,  the  conditions  of  this         \o[ 
experiment  are  varied,  it  will  be  seen  that 
these  results  are  of  but  little  value.    The 
following  will  make  this  clear. 

(a)  If  one  end   of  a  bar  magnet  be 
rounded  and  the  other  be  squared,  the 
rounded  end  will  lift  a  greater  weight  than 

the  squared  end,  and  this  although  it  can  Fig.  56. 

be  shown  that  the  two  ends  are  of  equal  magnetism.    The  weight 

lifted  therefore  varies  with  the  shape  of  the  pole. 

(b)  If  the  magnet  be  bent  into  a  horseshoe  shape  so  that  both 
poles  concur  in  the  lifting,  instead  of  the  weight  being  just  twice 


94  ELEMENTS  OF  ELECTRICITY. 

what  it  was  before  for  a  single  pole,  it  may  be  three  or  even  four 
times  greater.  The  weight  lifted  therefore  varies  with  the  shape 
of  the  magnet. 

(c)  If  the  weight  be  applied  very  gradually  the  magnet  will 
support  more  than  it  would  if  it  were  applied  suddenly.     If  a 
magnet  be  loaded  to  nearly  the  maximum  point  and  the  load  be 
left  hi  position  for  a  day,  the  weight  may  then  be  gradually  in- 
creased until  it  considerably  exceeds  the  original  maximum.    Once, 
however,  that  the  armature  is  torn  away,  the  lifting  power  of  the 
magnet  drops  back  to  what  it  was  formerly. 

(d)  Within  certain  limits,  the  larger  the  armature  the  greater 
the  weight  lifted. 

(e)  The  weight  lifted  varies  with  the  character  of  the  iron  or 
steel  of  which  the  armature  is  composed. 

(f)  Retaining  the  same  weight  and  compositon,   a  greater 
weight  will  be  lifted  if  the  armature  be  of  a  compact  shape,  such 
as  a  cube,  than  if  it  be  a  flat  disc.    The  weight  lifted  therefore 
varies  with  the  size  and  shape  of  the  armature. 

In  the  last  four  cases  above  we  see  that  although  the  magnet 
itself  does  not  vary,  the  weight  lifted  fluctuates  through  a  wide 
range.  We  can  not  say  which  of  these  weights  should  be  taken 
to  measure  the  strength  of  the  magnet  nor  is  it  practicable  to  give 
mathematical  expression  to  the  heterogeneous  conditions  enu- 
merated and  deduce  formulae  from  which  this  strength  might 
be  calculated.  What  we  have  done  therefore  is  not  to  measure 
the  strength  of  the  magnet  but  its  lifting  power  under  certain  given 
conditions. 

A  small  bar  magnet  should  lift  from  15  to  25  times  its  own 
weight.  In  the  Paris  Exhibition  of  1882  there  was  shown  a  magnet 
which  supported  76  times  its  own  weight.  Thompson  states  that 
the  lifting  power  of  a  good  steel  magnet  may  amount  to  40  pounds 
per  square  inch  of  pole  surface.  Electro-magnets,  to  be  described 
later,  are  much  more  powerful,  the  lifting  power  reaching  200 
pounds  per  square  inch. 

125.  Strength  of  Magnets.— If  we  examine  the  force  with 
which  one  magnet  attracts  or  repels  another,  the  two  being  at 
some  distance  apart,  we  find  that  it  is  not  affected  by  shape  of 
poles  or  length  of  exposure  to  each  other's  influence,  etc.,  but  is 
to  a  great  extent  independent  of  the  varying  conditions  mentioned 
in  the  preceding  paragraph.  The  force  with  which  magnetic  poles, 


MAGNETISM. 


95 


interact  is  therefore  selected  as  the  measure  of  their  strength.  We 
are  thus  naturally  led  to  enquire  what  is  precisely  a  magnetic  pole 
and  how  is  the  force  between  two  poles  measured. 

126.  Magnetic  Pole  Defined. — In  the  preceding  pages  we  have 
used  the  word  pole  to  designate  rather  vaguely  the  terminal  por- 
tions of  a  magnet,  the  regions  in  which  the  magnetic  force  is  most 
marked.  In  mathematical  discussions  it  is  desirable  to  treat  a 
pole  as  if  it  were  a  focus  or  the  point  of  application  of  the  resultant 
of  the  magnetic  forces  at  that  particular  end  of  the  magnet.  This 
point  may  be  approximately  located  as  follows.  In  a  bar  magnet 
the  magnetic  forces  are  symmetrically  distributed  around  its  axis 
and  the  pole  must  consequently  lie  upon  this  axis.  In  Fig.  57  let 
MN  represent  one-half  of  the  bar  magnet  which  is  supported 


N 


Fig.  57. 


horizontally.  With  a  pencil  mark  off  this  half  in  equal  divisions. 
Cut  a  small  soft  iron  wire  into  a  number  of  short  pieces  of  equal 
length  (and  hence  of  equal  weight).  Apply  the  end  of  one  of  these 
pieces  to  one  of  the  divisions  of  the  bar  and  then  other  pieces  to 
the  first  piece  until  the  accumulated  cluster  drops  off  of  its  own 
weight.  Note  the  particular  division  and  the  corresponding 
number  of  pieces.  Repeat  this  for  each  of  the  divisions,  then 
construct  a  curve  MEN  in  which  the  divisions  are  the  abscissae 
and  the  ordinates  are  laid  off  to  a  scale  to  represent  the  number  of 
pieces  of  wire  supported.  The  pole  is  on  the  axis  of  the  magnet 
and  approximately  opposite  the  center  of  gravity  of  the  tri- 
angular figure  MEN. 


96  ELEMENTS  OF  ELECTRICITY. 

In  short  thick  magnets  the  poles  are  distributed  over  a  con- 
siderable area  but  for  long  slender  bars  they  approach  the  ends 
and  approximate  the  hypothetical  point  or  focus.  According  to 
Fleming,  the  poles  of  a  bar  magnet  are  about  one-twelfth  of  its 
length  from  the  ends.  For  shorter  and  thicker  bars  this  distance 
may  amount  to  one-sixth  or  even  one-fifth. 

It  will  be  shown  later  (Par.  146)  that  for  certain  magnetic 
measurements  the  exact  location  of  the  pole  is  immaterial. 

Although  it  is  impossible  to  get  a  magnetic  pole  unaccompanied 
by  an  equal  and  opposite  pole,  yet  in  a  long  slender  magnet  the 
poles  are  so  far  apart  that  in  many  experiments  the  effect  of  the 
more  distant  one  may  be  neglected  and  the  results  are  as  if  we 
were  dealing  with  a  single  or  "free"  pole. 

127.  Measurement  of  Magnetic  Forces. — The  measurement  of 
magnetic  forces  is  not  entirely  a  simple  matter.  Two  magnets, 
A  and  B,  exposed  so  each  other's  influence  are  each  acted  upon  by 
four  forces.  The  north  pole  of  A  is  repelled  by  the  north  pole  of 
B  and  attracted  by  its  south  pole;  the  south  pole  of  A  is  repelled 
by  the  south  pole  of  B  and  attracted  by  its  north  pole.  In  addi- 
tion, each  magnet  is  acted  upon  by  the  earth's  magnetic  poles  so 
that  each  is  subject  to  eight  forces. 

In  most  cases  the  forces  are  comparatively  feeble.  They  must 
therefore  be  measured  by  comparing  them  with,  or  by  balancing 
them  against,  other  forces,  likewise  feeble,  whose  variation  follows 
some  readily  determined  law.  The  forces  used  for  comparison 
are — 

(a)  A  known  magnetic  force,  usually  that  of  the  earth.    There 
are  two  methods  of  comparison,  both  of  which  will  shortly  be 
described  (Pars.  129,  146). 

(b)  The  torsion  of  a  suspending  thread,  as  in  Coulomb's  torsion 
balance,  already  described  (Par.  52).    The  law  in  this  case  is  that 
the  force  varies  directly  as  the  angle  through  which  the  thread  is 
twisted. 

(c)  The  force  of  gravity  applied  through  a  bifilar  suspension. 
A  magnet  is  suspended  in  a  horizontal  position  by  two  parallel 
threads.    If  it  be  deflected  the  threads  must  be  twisted  from  a 
vertical  to  an  oblique  position  and  the  magnet  must  therefore  be 
raised.    The  law  in  this  case  is  that  the  force  varies  directly  as  the 
sine  of  the  angle  through  which  the  magnet  is  twisted. 


MAGNETISM.  97 

128.  Coulomb's  Second  Law. — The  second  law  of  magnetic 
force  comprises  two  statements.  First,  the  force  exerted  between 
two  magnetic  poles  varies  directly  with  the  product  of  their 
strengths,  and  second,  this  force  varies  inversely  as  the  square  of 
the  distance  separating  them.  The  distance  between  the  poles  is 
supposed  to  be  so  great  that  they  may  be  regarded  as  points. 

The  first  of  these  statements  hardly  requires  proof  since  it 
follows  at  once  from  the  fact  that  the  action  between  poles  is 
mutual  and  that  if  we  double  or  treble  the  strength  of  either  one 
we  double  or  treble  the  force  exerted  between  them.  Its  truth 
may  easily  be  shown  experimentally.  The  second  statement 
is  proved  experimentally  by  one  of  the  methods  now  to  be 
described. 


129.  Method  by  Oscillations. — From  mechanics,  the  time  of 
oscillation  of  a  simple  pendulum,  its  angular  displacement  being 
small,  is  given  by  the  equation 

I 
9 


-*»v 


in  which  I  is  the  length  of 

the  pendulum  and  g  is  the  acceleration  due  to  gravity.  The  force 
acting  upon  the  pendulum  is  mg,  m  being  its  mass.  The  above 
expression  may  be  written 


—     V  mg          V  force 
whence 

Force  =  ^~  =  constant  X  ^ 

But  \  is  the  number  of  oscillations  n  in  a  unit  of  time,  hence 
Force  =  constant  Xft2, 

or  the  force  producing 

pendular  vibrations  is  proportional  to  the  square  of  the  number 
of  vibrations  executed  in  a  unit  of  time.  Any  convenient  inter- 
val of  time  may  be  taken  as  the  unit. 

If  a  magnetic  needle  AB  (Fig.  58),  whose  position  of  rest  is 
along  the  magnetic  meridian  NS,  be  pushed  aside  through  an 
angle  5  and  then  released,  it  will  be  acted  upon  by  forces  tending 


98  ELEMENTS  OF  ELECTRICITY. 

to  return  it  to  its  primary  position  but  in  swinging  back  it  will 
acquire  a  momentum  which  will  carry  it  very  nearly  an  equal 
angular  distance  beyond  NS  and  will  then  swing 
in  the  opposite  direction  and  so  on,  that  is,  the 
needle  will  act  as  a  double  pendulum  in  a  hori- 
zontal plane  and  if  8  be  small  will  execute  oscil- 
lations whose  period  is  practically  constant.  The 
forces  which  tend  to  restore  the  needle  to  its  posi- 
tion in  the  meridian  are  due  to  the  interaction  of 
the  poles  of  the  magnet  and  those  of  the  earth. 
The  earth  being  a  sphere  and  its  poles  being 
located  beneath  its  surface,  their  action  lines  are 
oblique  to  the  plane  of  oscillation  of  the  needle 
and  only  the  horizontal  component  of  the  forces 
along  these  lines  affects  the  oscillations.  This 
horizontal  component  of  the  earth's  magnetism 
is  usually  designated  by  the  letter  H.  Within  the 
limits  of  space  covered  by  the  average  experiment  H  is  constant. 
If  the  strength  of  the  poles  of  the  needle  be  represented  by  m,  the 
force  acting  upon  each  pole  will  be  mH,  represented  in  Fig.  58  by 
AD  and  BC  and,  from  what  we  have  seen  above,  this  force  is  pro- 
portional to  the  square  of  the  number  of  oscillations  executed  by 
the  needle  in  a  given  time.  How  this  principle  may  be  utilized  in 
measurements  will  be  shown  in  Par.  131. 

130.  Magnetic  Moment. — The  active  components  of  the  forces 
AD  and  BC  (Fig.  58)  are  AE  and  BF,  each  of  which  is  equal 
to  m.  H.sm8.      These   constitute   a   couple   whose   moment  is 
m.H.smd.l,  I  being  the  distance  between  the  two  poles.    The 
product  ml  is  called  the  magnetic  moment  of  the  needle  and  in 
formulae  is  represented  by  M.    Although  the  exact  position  of 
the  poles,  and  consequently  the  distance  I,  is  most  often  unknown, 
M  itself  may  be  determined  by  experiment  and  is  used  in  certain 
magnetic  measurements  to  be  described  later  (Pars.  148, 149, 150). 

131.  Experimental    Proof   of   Law    of   Inverse    Squares. — In 

Fig.  59,  A  is  a  very  small  magnet,  less  than  half  an  inch  in  length, 
suspended  in  a  paper  stirrup  by  a  single  fibre  of  unspun  silk  and 
at  rest  in  the  magnetic  meridian.  The  resistance  of  the  silk  fibre 
being  very  slight,  if  the  magnet  be  started  in  oscillation  it  will 
continue  so  for  from  five  to  ten  minutes.  It  is  given  a  slight  im- 


MAGNETISM.  99 

pulse  and  the  number  of  oscillations  executed  in  a  given  interval, 
say  one  minute,  is  counted.  Suppose  this  number  to  be  10.  A 
slender  bar  magnet  B  is  now  placed  in  the  same  meridian,  its  axis 
in  the  prolongation  of  the  axis  of  A.  (This  experiment  may  also 
be  performed  with  the  magnet  B  in  a  vertical  position,  its  pole 
being  in  the  meridian  and  horizontal  plane  of  A.)  B  must  be 
placed  at  such  distance  from  A  that  for  small  angular  deviations 
of  A  the  action  lines  of  B  are  sensibly  parallel.  This  is  also  one  of 
the  reasons  for  keeping  A  very  small,  the  other  being  that  if  A  be 
small  its  poles  are  more  nearly  the  same  distance  from  the  pole  of 
B.  A  is  again  set  in  motion  and  if  the  poles  of  the  bar  magnet 


Fig.  59. 

coincide  in  direction  with  those  of  A,  the  oscillations  will  be  more 
rapid.  Suppose  that  now  12  are  executed  in  one  minute.  The 
force  due  to  the  horizontal  component  of  the  earth's  magnetism 
is  to  the  combined  force  of  this  component  and  that  of  the  pole  of 
B  as  100  is  to  144.  Let  B  now  be  pushed  up  towards  A  until  the 
distance  between  its  pole  and  that  of  A  has  been  halved.  A  set  in 
motion  will  now  be  found  to  execute  about  16.5  oscillations  per 
minute.  The  total  force  upon  A  in  the  first  place  is  to  that  in  the 
second  as  (12)2  is  to  (16.5)2  or  as  144  is  to  272.  The  force  due  to  B 
alone  is  as  (144-100)  is  to  (272-100)  or  as  44  is  to  172,  which  is 
very  nearly  as  1  is  to  4.  In  other  words,  as  the  distance  is  halved 
the  force  is  quadrupled,  which  is  in  accordance  with  the  law  of 
inverse  squares. 

In  the  above  proof  the  distance  between  the  poles  of  the  two 
magnets  must  be  known  and  as  the  exact  position  of  the  poles 
themselves  is  not  precise,  their  distance  apart  is  apparently  un- 
certain; however,  this  distance  may  be  assumed  as  nearly  as  pos- 
sible and  one  or  two  trial  experiments  thereafter  will  show  what 
the  correct  distance  should  be. 

132.  Proof  of  Law  of  Inverse  Squares  by  Coulomb's  Balance. 

—Coulomb  also  proved  this  law  by  means  of  the  balance  which 
bears  his  name.  A  description  of  the  actual  experiment  would  be 


100  ELEMENTS  OF  ELECTRICITY. 

somewhat  long  and  it  will  suffice  to  say  that  in  the  apparatus  as 
represented  in  Fig.  22,  a  slender  bar  magnet  took  the  place  of  the 
shellac  needle  G  and  a  second  one  took  that  of  KH.  The  instru- 
ment was  set  up  so  that  with  no  torsion  on  the  suspending  fibre, 
the  horizontal  needle  and  the  opening  K  in  the  glass  cover  lay  in 
the  same  magnetic  meridian.  The  experiment  was  then  conducted 
as  explained  in  Par.  52,  due  allowance  being  made  for  the  effect  of 
the  earth's  magnetism. 

133.  Unit  Magnetic  Pole.  —  Magnetic  poles  differ  in  strength. 
We  may  consider  that  there  is  more  magnetism  concentrated  at 
the  stronger  pole  or  may  assume  that  there  are  magnetic  poles  of 
unit  strength  and  that  a  greater  number  of  these  are  gathered  at 
the  stronger  pole.  A  definite  conception  of  a  unit  pole  may  be 
obtained  from  the  following.  Coulomb's  second  law  may  be 
expressed  thus, 

f  _  m  X  m' 
J  ''    ~~¥~ 

in   which,    since   we   are 

using  the  C.  G.  S.  system,  /is  the  force  in  dynes  between  the  poles, 
m  and  mf  the  strength  of  the  respective  poles  and  d  their  distance 
apart  in  centimeters.  If  the  poles  be  of  equal  strength  this 
becomes 


Finally,  if  /  becomes  one  dyne  and  d  one  centimeter,  we  have 
w  =  l,  or  a  unit  magnetic  pole  is  that  pole  which  when  placed  at  a 
distance  of  one  centimeter  from  a  similar  and  equal  pole  repels  it 
with  a  force  of  one  dyne. 


MAGNETISM.  101 


CHAPTER  14. 
THE   MAGNETIC   FIELD. 

134.  Magnetic  Field.— In  the  space  around  a  magnet  all  poles 
experience  forces  of  attraction  and  of  repulsion  and  this  space  is 
called  the  field  of  the  magnet.    As  we  recede  from  the  magnet 
these  forces  diminish  in  accordance  with  the  law  of  inverse  squares 
and,  to  fix  its  limits  more  definitely,  we  define  a  magnetic  field  as 
that  space  surrounding  a  magnet  in  which  magnetic  force  due  to 
this  magnet  is  perceptible. 

135.  Direction  of  Magnetic  Field. — As  an  aid  to  the  conception 
of  a  magnetic  field  we  may  resort  to  the  same  analogy  as  in  the  case 
of  the  electric  field  (Par.  58)  and  compare  it  to  a  current  of  water. 
In  a  magnetic  field  there  is  no  matter  in  actual  movement  but 
there  is  in  a  certain  sense  a  flow  of  force  and  magnetic  poles,  placed 
in  the  field,  are  swept  along  just  as  light  objects  are  carried  by  a 
stream.     Since  free  north  poles  would  be  carried  along  in  one 
direction  and  free  south  poles  in  the  opposite  direction  we  by 
convention  define  the  positive  direction  of  a  magnetic  field  as  that 
direction  in  which  a  free  north  pole  would  move. 

136.  Intensity  of  Magnetic  Field. — Just  as  we  might  measure 
the  strength  of  a  current  by  the  force  with  which  it  pushes  a  board 
of  unit  area  placed  in  it,  so  we  agree  to  measure  the  intensity  of  a 
magnetic  field  by  the  force  with  which  it  acts  upon  a  unit  pole 
placed  in  it  and  we  define  a  unit  magnetic  field  as  that  field  which 
acts  with  a  force  of  one  dyne  upon  a  unit  pole  placed  in  it.    If  we 
say  that  a  magnetic  field  has  a  strength  of  three,  we  mean  that  it 
will  act  with  a  force  of  three  dynes  upon  a  unit  pole  placed  in  it. 
If  the  strength  of  the  field  be  H  and  that  of  the  pole  be  m,  the 
force  with  which  the  field  acts  upon  the  pole  is  Hm  dynes.    From 
the  foregoing  and  from  Par.  128  it  follows  that  the  field  at  a  dis- 
tance d  from  a  pole  of  strength  m  is  m/d2. 

137.  Magnetic  Lines  of  Force.— In  Fig.  60  let  P  be  a  point  in 
the  field  of  the  bar  magnet  NS  and  for  simplicity  of  construction 
suppose  that  at  this  point  the  distance  SP  is  twice  the  distance 


102  ELEMENTS  OF  ELECTRICITY. 

NP.  Suppose  a  free  north  pole  to  be  placed  at  the  point  P.  It 
will  be  repelled  from  N  along  NP  and  attracted  towards  S  along 
PS.  In  the  case  assumed  the  distance  NP  being  only  one-half  of 
PS,  by  the  law  of  inverse  squares  the  repulsion  along  NP  is  four 


J  Fig.  60.  V 

times  as  great  as  the  attraction  along  PS.  Lay  off  PB  any  con- 
venient distance  and  PA  four  times  as  great  and  complete  the 
parallelogram.  PR  is  the  resultant  at  the  point  P  of  the  magnetic 
forces  of  the  two  poles  N  and  S  or,  in  other  words,  the  free  north 
pole  at  P  will  be  urged  along  the  resultant  PR  with  a  force  pro- 
portional to  PR. 

Suppose  this  free  north  pole  to  move  along  PR  a  very  small 
distance.  In  doing  so  it  will  move  away  from  N  more  rapidly 
than  it  does  from  S.  This  will  cause  the  repulsion  from  N  to  grow 
weaker  and  the  attraction  to  S  to  grow  relatively  stronger  and  the 
path  of  the  pole  will  bend  around  towards  S.  In  its  successive 
positions  therefore,  the  pole  will  follow  a  curve  which  at  every 
point  indicates  by  its  direction  the  direction  of  the  resultant  of 
the  magnetic  forces  at  that  point.  This  curve  is  called  a  magnetic 
line  of  force. 

If  instead  of  a  free  north  pole  a  free  south  pole  had  been  placed 
at  P,  it  would  have  been  urged  with  an  exactly  equal  force  in  an 
exactly  opposite  direction  PR',  and  in  its  path  would  have  traced 
out  the  same  curved  line  but  in  a  reverse  direction.  By  convention 
(Par.  135)  we  define  the  positive  direction  of  a  magnetic  line  of 
force  as  that  direction  in  which  a  free  north  pole  would  move.  In 


MAGNETISM. 


103 


our  diagrams  the  positive  direction  of  these  lines  is  always  in- 
dicated by  an  arrowhead  placed  upon  the  lines. 

138.  Mapping  Lines  of  Force. — If  at  any  point  P  (Fig.  60) 
there  be  placed  a  very  small  magnetic  needle,  its  north  pole  would 
be  urged  in  the  direction  PR,  its  south  pole  in  the  direction  PR', 
and  the  needle  will  take  up  a  position  approximately  tangent  to 
the  line  of  force  at  the  point  P.  If  a  sufficient  number  of  these 
little  needles  be  placed  one  after  the  other,  as  shown  in  Fig.  60, 


»)  -.  . '  ;:  /^  :>.^VV:\s  ~-«r\vT:--  •*  '//'->£  ',#>•£  ,>;':'    A; ' . '  "^ 

•.  *:/:;.  .;\-J:Aii>  ^   z-* -'^;*-:^  *'*-?*.'&*..•&•;  4  \^*  ' 

Fig.  61. 


the  successive  tangents  which  they  indicate  will  serve  as  an  enve- 
lope and  will  mark  out  the  line  of  force,  approximating  more  and 
more  closely  to  it  as  their  length  is  decreased  and  number  increased. 
Finally,  if  the  entire  space  about  the  magnet  were  strewn  closely 
with  the  little  needles  a  number  of  lines  of  force  would  be 
traced. 

This  condition  may  be  realized  practically  as  follows.  A  sheet 
of  glass,  of  stiff  paper  or  of  any  non-magnetic  body  is  placed  upon 
a  magnet  and  is  then  sprinkled  with  fine  iron  filings.  From  what 
we  have  already  seen  (Par.  120)  each  individual  filing  becomes  for 
the  time  being  a  magnet,  but  these  little  magnets  are  not  free  to 


104  ELEMENTS  OF  ELECTRICITY. 

move  since  their  weight  holds  them  with  friction  against  the  sur- 
face over  which  they  are  sprinkled.  If  the  sheet  be  given  a  gentle 
tap  the  filings  are  jarred  and  for  a  minute  interval  of  time  are 
bounced  up  into  the  air.  Being  now  freed  from  the  friction  which 
held  them  in  place,  they  move  under  the  influence  of  the  magnetic 
forces  and  after  a  few  repetitions  of  the  jarring  they  gather  along 
well  marked  lines  as  shown  in  Fig.  61. 

139.  Permanent  Record  of  Magnetic  Figures. — Several  ways 
have  been  described  by  which  these  magnetic  figures,  or  curves 
traced  by  the  filings,  may  be  recorded  permanently.    The  following 
is  simple  and  convenient.    Upon  a  soft  pine  board  about  a  foot 
square  the  magnet  is  placed  and  its  outline  is  traced  with  a  pencil. 
With  a  chisel  this  outline  is  then  hollowed  out  until  when  in  posi- 
tion the  upper  surface  of  the  magnet  is  on  a  level  with  that  of  the 
board.    The  board  is  then  taken  into  a  subdued  light  and  there  is 
pinned  upon  it,  prepared  surface  up,  a  sheet  of  blue-print  paper 
about  8  XlO  inches.    Iron  filings  are  then  sprinkled  over  this  paper 
and  the  board  is  tapped  on  the  under  side  until  the  magnetic 
figures  come  out  as  desired.    Better  results  are  obtained  if  before 
using  the  filings  they  are  passed  through  two  sieves,  one  to  separate 
the  dust-like  particles  and  the  other  those  of  too  large  size.    The 
board  with  the  filings  in  position  is  then  exposed  in  a  strong 
sunlight   for  from  three  to  five   minutes,   the   rays   falling  as 
nearly  perpendicular  to  the  paper  as  possible.    It  is  then  carried 
back  to  the  subdued  light,  the  filings  poured  off  and  the  paper 
thoroughly  washed  in  clear  water.    The  resulting  blue-print  is 
then  dried. 

140.  Use  of  Magnetic  Figures. — These  magnetic  figures  are  of 
assistance  in  the  study  of  magnetic  fields  and  often  enable  us  to 
grasp  at  a  glance  conditions  which  might  otherwise  require  con- 
siderable mathematical  analysis  to  develop.    For  example,  they 
show  in  a  striking  manner  how  the  field  between  two  mutually 
attracting  poles  differs  from  that  between  two  that  mutually 
repel.    Fig.  62  represents  the  field  between  two  dissimilar  poles. 
In  this  the  lines  of  force  are  seen  to  pass  from  one  to  the  other  as 
if  pulling  them  together.    At  the  same  time  these  lines  are  bowed 
out  revealing  the  existence  of  the  crosswise  pressure  causing  them 
to  separate.    Fig.  63  shows  the  field  between  two  similar  poles  and 
it  does  not  require  a  great  stretch  of  the  imagination  to  conceive 


MAGNETISM. 


105 


of  the  lines  of  force  as  hands  placed  palm  against  palm  and  pushing 
each  other  back.  Further  examples  of  the  use  of  these  figures  will 
be  met  in  subsequent  pages. 


Fig.  62. 


Fig.  63. 

141.  Compounding  Magnetic  Fields. — The  magnetic  fields 
hitherto  considered  are  those  surrounding  a  single  pole  or  pair  of 
poles  and  are  symmetrical  with  respect  to  the  single  pole  or  to  the 
line  joining  the  two  poles.  Should  these  fields  be  intersected  by 
another,  the  resultant  field  would  be  obtained  by  compounding 


106 


ELEMENTS  OF  ELECTRICITY. 


the  two  and  would  in  general  be  unsymmetrical.  The  earth's 
field  most  often  produces  distortion  in  others  but  its  strength 
being  comparatively  feeble,  the  distortion  is  not  revealed  in  the 
magnetic  figures  produced  with  filings.  If,  however,  the  field  be 
mapped  as  follows  the  effect  of  the  earth's  field  becomes  evident. 
Place  a  bar  magnet  in  the  center  of  a  sheet  of  paper  and  then  in 
contact  with  the  magnet  place  one  of  the  little  compass  needles  one 
centimeter  in  length  and  mounted  in  a  glass-covered  brass  case. 
With  a  pencil  make  a  dot  at  the  far  end  of  the  needle,  then  shift 
the  compass  until  the  near  end  of  the  needle  is  over  this  dot  and 


Fig.  64. 

r 

again  make  a  dot  at  the  new  position  of  the  far  end  of  the  needle 
and  so  on  to  the  limits  of  the  paper.  Connect  these  dots  by  a 
continuous  curve.  Start  with  the  compass  at  some  other  point 
along  the  magnet  and  make  a  second  chain  of  dots  and  so  on  until 
the  whole  space  about  the  magnet  has  been  marked  off.  Figs.  64 
and  65  represent  fields  traced  in  this  way,  Fig.  64  with  the  north 
pole  of  the  bar  magnet  pointing  north,  Fig.  65  with  the  north  pole 
pointing  south.  In  each  case  immediately  around  the  magnet 
the  strength  of  its  field  overpowers  that  of  the  earth  but  the 
strength  of  the  magnet's  field  falls  off  rapidly  as  the  distance  from 
it  increases  while  the  earth's  field  is  constant  over  a  considerable 


MAGNETISM. 


107 


area  and  at  a  distance  from  the  magnet  the  earth's  field  has  the 
ascendancy.  At  the  spots  marked  P  these  two  forces  neutralize 
each  other  and  the  needle  will  vacillate  and  come  to  rest  in  any 
position.  These  two  figures,  though  different,  are  both  symmet- 
rical since  the  bar  magnet  was  designedly  placed  in  a  north  and 
south  position.  Should  it  be  placed  in  any  oblique  position  the 
symmetry  will  be  destroyed. 


'Fig.  65. 

142.  Properties  of  Magnetic  Lines  of  Force. — In  some  of 
their  properties  magnetic  lines  of  force  are  similar  to  electric  lines 
of  force  but  in  others  they  differ  widely.  They  agree  with  electric 
lines  of  force  in  having  a  tension  along  their  length,  or  a  tendency 
to  shorten,  and  also  a  pressure  at  right  angles.  They  also  never 
intersect.  They  differ  from  electric  lines  of  force  in  that  they  are 
closed  curves,  that  they  penetrate  all  substances  whether  con- 
ductors or  not  and  that  they  do  not  necessarily,  or  even  generally, 
leave  or  enter  a  surface  at  right  angles.  Being  a  closed  curve,  a 
complete  magnetic  line  of  force  lies  partly  in  the  magnet  and 
partly  in  the  surrounding  medium.  While  the  majority  of  these 
lines  emerge  near  the  poles,  many,  as  shown  in  Figs.  61  and  66, 
emerge  along  the  sides  of  the  magnet.  The  lines  within  the  magnet 


108  ELEMENTS  OF  ELECTRICITY. 

are  designated  collectively  as  the  magnetic  flux  ana  this  flux  is 
evidently  a  maximum  at  the  mid-section  of  the  magnet.  This 
is  sometimes  otherwise  expressed  by  saying  that  the  intrinsic 
magnetism  is  a  maximum  at  this  mid-section.  The  intrinsic 
magnetism  is  of  no  effect  on  outside  bodies.  Magnetic  effects 
of  attraction  and  repulsion  are  produced  only  by  those  lines  of 
force  which  emerge  from  the  magnet.  This  is  called  the  free 
magnetism  and  is  greatest  in  the  neighborhood  of  the  poles. 


Fig.  66. 

It  must  be  noted  here  that  that  portion  of  these  lines  which  lies 
within  the  magnet  does  not  conform  to  the  definition  of  a  line  of 
force  as  given  in  Par.  137,  for  which  reason  these  internal  lines 
have  been  variously  designated  as  lines  of  magnetization,  lines 
of  magnetic  induction,  etc.  An  internal  line  of  magnetization  is, 
however,  always  the  continuation  of  an  external  line  of  force  and 
the  above  distinction,  although  academically  correct,  is  without 
practical  importance.  This  fact  will  be  brought  out  more  clearly 
in  the  subject  of  electro-magnetics. 

That  portion  of  a  magnetic  body  from  which  lines  of  force 
emerge  is  always  a  north  pole  and  that  portion  of  such  body  into 
which  they  enter  is  always  a  south  pole.  To  this  rule  there  is  but 
one  exception.  The  lines  of  force  of  the  earth  enter  at  the  north 
magnetic  pole  and  come  out  at  the  south  magnetic  pole.  The 
reason  for  this  exception  has  already  been  given  (Par.  117). 

143.  Magnetic  Lines  Pass  Preferably  Through  Magnetic 
Substances. — If  in  the  space  between  the  two  dissimilar  poles  in 
Fig.  62  there  be  inserted  a  soft  iron  block  and  a  magnetic  figure 
be  then  taken,  the  lines  of  force  which  in  Fig.  62  curved  out  widely 
will  now  be  seen  to  have  drawn  in,  as  shown  in  Fig.  67,  and  pass 
through  the  iron  block  instead  of  through  the  air.  A  simple  ex- 
planation is  that  the  iron  block  has  become  a  magnet  by  induction 
and  the  lines  of  force  converge  to  the  nearest  poles,  but  it  is  some- 
times conveniently  explained  by  the  statement  that  magnetic 


MAGNETISM. 


109 


lines  of  force  travel  by  preference  through  magnetic  bodies  and 
will  avail  themselves  of  such  a  path  whenever  the  opportunity 
offers.  This  principle  affords  an  explanation  of  certain  phenomena 
and  is  of  considerable  practical  importance. 


Fig.  67. 

It  has  already  been  noted  (Par.  112)  that  filings  cling  to  the 
edges  of  a  magnet  rather  than  to  the  flat  surfaces.  This  fact  is 
also  clearly  shown  in  Figs.  61,  62  and  63.  In  Fig.  68,  a  and  b 
represent  end  views  of  a  bar  magnet.  If  the  lines  of  force  radiated 
equally  from  the  internal  pole  they  would  emerge  as  shown  in  a 
and  there  would  be  more  filings  just  on  top  of  the  magnet  than 
elsewhere  since  this  point  is  nearest  to  the  pole  and  consequently 


Fig.  68. 

at  this  point  the  attraction  would  be  strongest.  But  since  the 
lines  prefer  to  travel  as  far  as  possible  through  the  steel,  their 
actual  path  is  as  represented  in  b  and  the  filings  are  thickest 
where  the  lines  of  force  are  thickest,  that  is,  along  the  edges. 

An  essential  part  of  dynamos  and  motors  consists  in  its  simplest 
form  of  two  powerful  magnetic  poles  embracing  between  them  a 
cylindrical  opening.  It  is  highly  important  that  there  should  be  a 


110 


ELEMENTS  OF  ELECTRICITY. 


uniform  field  along  the  faces  of  these  magnets  but  owing  to  the 
principle  above,  the  lines  of  force,  as  shown  in  Fig.  69  a,  crowd 
across  at  the  top  and  bottom  and  leave  the  central  portion  of  the 
opening  thin.  If,  however,  there  be  inserted  in  this  space  a  soft 


Fig.  69. 


iron  cylinder,  the  lines  will  pass  through  this  cylinder  and,  as 
shown  in  b,  will  produce  along  the  pole  faces  a  dense  and  uniform 
field. 

If  a  magnet  NS  (Fig.  70)  produces  a  deflection  in  a  needle  A, 
the  needle  can  be  screened  from  this  effect  by  interposing  between 


5    \ 


Fig.  70. 

it  and  the  magnet  a  comparatively  thick  iron  plate  B.  The  lines 
of  force  from  N,  which  formerly  reached  A,  now  travel  through 
B,  as  shown  in  the  figure,  and  thence  back  to  S.  If  A  be  placed 
inside  of  an  iron  cylinder  it  may  be  entirely  screened  from  outside 
magnetic  influences. 


MAGNETISM. 


Ill 


If  a  pivoted  iron  bar  AB  (Fig.  71)  be  placed  diagonally  across 
a  magnetic  field  NS  it  will  swing  so  as  to  place  itself  parallel  to 
the  field.  We  may  explain  this  motion  as 
follows.  The  lines  of  force  of  the  field,  from 
what  we  have  just  seen,  turn  to  one  side  and, 
as  shown  in  the  figure,  run  lengthwise 
through  the  bar.  The  tension  along  these 
lines  produces  a  couple  on  AB  which  pulls 
it  around  to  parallelism  with  NS.  The  law 
under  which  this  movement  takes  place  is 
that  a  magnetic  body  placed  in  a  magnetic 
field  tends  to  move  so  that  its  longest  axis 
coincides  in  direction  with  the  lines  of  force 
of  the  field. 

144.  Law  of  Maximum  Flux. — In  Fig.  72, 
A  is  a  piece  of  soft  iron  in  a  weak  field  to 

one  side  of  the  strong  field  B.  The  lines  of  force  of  the  strong 
field  move  out,  as  shown  in  the  figure,  so  as  to  pass  through 

A  and  if  A  be  free  to  move  it  will  be 
drawn  over  into  the  denser  field  at  B. 
If  A  be  a  magnet  placed  obliquely  to  B 
it  will  be  both  drawn  over  into  B  and 
turned  so  that  its  own  lines  of  force  will 
be  parallel  to  and  of  the  same  direction 
as  those  of  B.  It  will  therefore  embrace 
in  lengthwise  direction  both  its  own 
lines  of  force  and  those  of  the  field  B,  or, 
in  general,  a  magnetic  body  placed  in  a 
magnetic  field  tends  to  move  so  as  to 
embrace  in  one  direction  the  maximum 
number  of  lines  of  force.  This  is  but  a 
particular  case  of  Maxwell's  Law,  a  prin- 
ciple of  great  importance  which  will  be  discussed  later  (Par.  371). 

145.  Graphic  Representation  of  Intensity  of  Magnetic  Field. — 

For  the  same  reasons  as  given  in  Par.  61,  it  has  been  agreed  to 
represent  graphically  the  intensity  of  a  magnetic  field  by  the 
number  of  lines  of  force  per  square  centimeter  taken  perpendicular 
to  these  lines.  From  this  standpoint,  a  unit  magnetic  field  is 
defined  as  that  field  which  contains  one  line  of  force  per  square 


112 


ELEMENTS  OF  ELECTRICITY. 


centimeter  of  cross-section.  A  similar  course  of  reasoning  to  that 
given  in  Par.  63  will  lead  to  the  conclusion  that  there  radiate 
from  a  unit  pole  4  TT  lines  of  force. 

146.  Comparison  of  Magnetic  Fields.  Tangent  Law. — There 
are  a  number  of  ways  in  which  magnetic  fields  may  be  compared 
by  means  of  the  deflection  which  they  produce  in  a  magnetic  needle. 
If  a  needle  which  is  poised  in  the  meridian  be  exposed  to  such  a 
field  at  right  angles  to  the  meridian,  the  needle  will  be  deflected 
through  a  certain  angle.  The  field  draws  it  to  one  side  with  a 
decreasing  moment;  the  horizontal  component  of  the  earth's  mag- 
netism pulls  it  back  to  the  meridian  with  an  increasing  moment. 
A  position  of  equilibrium  is  finally  reached  and  the  angle  of 
deflection  may  be  read  from  a  scale  placed  beneath  the  needle. 

In  general,  in  instruments  which  operate  thus  by  a  needle 
moving  over  a  scale,  the  force  which  pulls  the  needle  away  from 
its  zero  position  is  called  the  deflecting  force;  the  force  which  tends 
to  restore  it  to  the  zero  position  is  called  the  controlling  force. 

In  the  following  method  it  is  assumed  that  the  action  lines  of 
the  magnetic  force  upon  the  poles  of  the  needle  are  parallel  and 
that  within  the  limits  of  the  space  over  which  the  needle  swings  the 
force  is  constant.  In  order  to  realize  this  condition  as  nearly  as 
possible  the  needle  is  made  very  small.  If  the  scale  of  degrees 
varied  with  the  size  of  the  needle  it  would  become  too  small  to  be 
read  with  much  accuracy,  therefore  an  auxiliary  pointer  of  alum- 
inum or  of  some  other  light  substance 
is  fastened  to  the  needle  and  a  larger 
scale  may  then  be  used. 

In  Fig.  73  let  A  B  be  a  magnetic 
needle  of  pole  strength  m,  deflected 
from  the  meridian  NS  through  an 
angle  8  by  a  magnetic  field  H '  act- 
ing at  right  angles  to  the  meridian. 
At  the  pole  A  the  controlling  force 
is  mH,  represented  by  AC.  The 
deflecting  force  is  mH',  represented 
by  AD.  An  exactly  similar  set  of 
forces  act  upon  the  pole  B  but  to 
consider  them  would  simply  be  to 
repeat  what  we  shall  prove  for  the  set  at  A.  The  controlling 
force  may  be  divided  into  two  components,  one,  AF,  in  the 


Fig.  73. 


> 


MAGNETISM.  113 

direction  of  the  axis  of  the  needle  and  of  no  effect  so  far  as 
rotation  is  concerned;  the  other,  A  E,  perpendicular  to  the  needle 
and  active  in  restoring  it  to  the  meridian.  From  Fig.  73, 

AE  =  AC.  sin  5  =  mH.&iud 

Similarly,  the  deflecting  force  may  be  divided  into  two  com- 
ponents, one  in  the  direction  AF,  the  other  AG,  which  =  AD.  cos  6 
=w#/.cos  5  and  which  is  active  in  deflecting  the  needle  from 
the  meridian.  When  the  needle  comes  to  rest  these  two  active 
components,  A  E  and  AG,  are  equal,  hence 

=  mH  .sinS 


whence  Hf  =  H  •          =  H  .  tanS 

cos  5 

or,  the  magnetic 

field  which  acting  at  right  angles  to  the  meridian  produces  in  a 
magnetic  needle  a  deflection  5,  is  equal  to  the  horizontal  component 
of  the  earth's  magnetism  at  that  point  multiplied  by  the  tangent 
of  the  angle  of  deflection. 

It  follows  direct  from  the  foregoing  that  different  magnetic 
fields  acting  at  right  angles  with  the  meridian  will  deflect  a 
needle  through  angles  whose  tangents  are  proportional  to  the 
respective  fields.  This  is  known  as  the  Tangent  Law  and  is  an 
important  principle  in  certain  electrical  measuring  instruments  to 
be  described  later  (Par.  373). 

It  will  be  noted  that  the  deflection  produced  is  independent  of 
the  strength  and  of  the  length  of  the  needle,  or  rather  of  the  dis- 
tance between  the  poles.  Hence,  as  was  stated  in  Par.  126,  the 
exact  location  of  the  poles  is  immaterial.  If,  however,  the  con- 
trolling force  be  non-magnetic  (as  in  Nobili's  astatic  galvanom- 
eter) these  factors  are  of  importance. 

147.  The  Sine  Law.  —  Should  the  deflecting  field  make  a  con- 
stant angle  with  the  needle  instead  of  with  the  meridian,  a  different 
state  of  affairs  would  result.  Whatever  the  constant  angle  may  be, 
we  can  always  divide  the  force  into  two  components,  one  of  which 
is  perpendicular  to  the  needle  and  is  the  effective  one  in  producing 
deflection.  We  may  therefore  in  Fig.  73  consider  AG  as  repre- 
senting the  deflecting  force  mH'.  When  equilibrium  is  reached 
AG  =  AE,  or 

mH'  =mH  .sin  5,  or  H'  =  H  .sin  5 

whence,  magnetic  fields  acting  at  a  constant  angle  with  the  needle 


114  ELEMENTS  OF  ELECTRICITY. 

are  to  each  other  as  the  sines  of  the  respective  angles  of  deflection. 
This  is  known  as  the  Sine  Law  and  is  the  principle  of  one  class  of 
galvanometers  (Par.  376). 

148.  Determination  of  the  Strength  of  a  Magnetic  Field.  —  In 
Pars.  129,  146  and  147,  principles  have  been  given  which  enable 
us  to  compare  magnetic  fields  among  themselves,  that  is,  to  deter- 
mine how  many  times  stronger  or  weaker  one  field  is  than  another, 
but  these  do  not  enable  us  to  make  any  absolute  measurement. 
The  following  method  of  determination  of  the  absolute  strength 
of  a  magnetic  field  is  due  to  Gauss. 

In  Par.  129  we  saw  that  the  time  of  oscillation  of  a  simple 
pendulum  is  given  by  the  expression 

T  =  2 


force 

Multiplying  the  expression  under  the  radical  sign  by  I  above 
and  below,  it  becomes 

m.l2 

I  X  force 

In  mechanics,  the  sum  of  the  product  of  the  mass  of  each  particle 
of  a  rotating  body  into  the  square  of  the  distance  of  the  particle 
from  the  axis  of  rotation  is  called  the  moment  of  inertia  of  the  body. 
In  the  above  expression  m  is  the  concentrated  mass  of  the  pendu- 
lum and  I  is  its  distance  from  the  point  of  suspension,  therefore, 
m  .I2  is  the  moment  of  inertia  of  the  pendulum.  Representing  this 
by  K,  the  above  becomes 

K 

I  X  force 

In  the  case  of  a  needle  in  a  magnetic  field,  the  force  is  m  .  H,  m 
now  representing  the  strength  of  the  pole  of  the  needle,  and  the 

above  may  be  written 

K 

l.m.  H 

But  (Par.  130)  l.m  is  the  magnetic  moment  of  the  needle,  hence 
the  expression  becomes 

K 

M.H 

The  expression  for  the  time  of  oscillation  may  therefore  be 
written 


MAGNETISM.  115 

In  this,  T  can  be  determined  by  observation  and  K  by  calcula- 
tion or  by  experiment.*  We  therefore  have  an  equation  involving 
two  unknown  quantities  M  and  H,  one  of  which,  H,  we  wish  to 
determine.  If  we  can  obtain  another  expression  involving  these 
same  two  quantities,  we  may  by  combination  determine  H.  The 
obtaining  of  this  second  expression  is  explained  in  the  two  follow- 
ing paragraphs. 

149.  Turning   Moment  of  One   Magnet  upon  Another. — Let 

ns  (Fig.  74)  be  a  small  magnetic  needle,  its  center  lying  on  the 
prolongation  of  the  axis  of  the  magnet  NS  and  its  length  perpen- 
dicular to  this  prolongation.  Let  m'  be  the  strength  of  the  poles 

A 

n 

o 


3-------- 

[Fig.  74. 


S 


of  ns  and  let  m  be  that  of  the  poles  of  NS.  Let  the  distance 
between  the  poles  of  ns  be  21  and  that  between  the  poles  of  NS 
be2L.  LeiOC  =  Da,udNn  =  d.  From  the  figure  d  =  Vl*+(D  -L)2. 
The  repulsion  between  N  and  n  is  m  .  m'/d2  and  the  moment  of  this 
force  upon  ns  is 


The  triangles  NOn  and  OnA  are  similar  since  they  are  both 
right  angled  and  have  a  common  angle  NnO,  hence 

OA  :  On  =  NO  :  Nn 
On  X  NO 


Hence  OA  = 


—  ^-~ 

Nn 

l(D  -  L) 
d 
l(D-L) 


(D-  L) 

*  The  moment  of  inertia  of  a  bar  magnet  is 

R=  /  (length)'  +(breadth)«\  x  magg 

that  of  a  cylindrical  magnet  is 


116  ELEMENTS  OF  ELECTRICITY. 

Hence  the  above  moment  is 

m .  m' .1  (D  -  L) 
[I*  +  (D-  L)2]? 

The  moment  of  N  on  s  is  the  same  and  the  total  moment  due 
to  AT  is 

2m.m'.l(D-L) 
[P  +  (D  -  L)2]* 

The  moment  due  to  S  is  found  in  the  same  manner  and  may  be 
obtained  direct  from  the  preceding  expression  by  substituting 
D+L  for  D  —  L.  Since  it  acts  in  the  opposite  direction  to  that 
due  to  N,  the  resultant  component  is 

2.m.m/ .l(D  -  L)  _  2.m.m' .l(D  +  L) 

[P  +  (D  -  L)2]*  [Z2  +  (D  +  L)2]* 

If  ns  be  very  small,  Z2  can  be  neglected  in  comparison  to  (D  —  L)2, 
and  consequently  also  in  comparison  to  (Z)+L)2,  and  the  above 
expression  can  be  written 

I  I 


2.m.m'.l 


or 


(D  -  L)2      (D  +  L)2 
DL 


Finally,  if  the  distance  between  the  two  magnets  be  so  great 
that  we  may  neglect  L2  as  compared  to  D2,  the  foregoing  becomes 

Sm.m'.l.L 

But  2mL  is  the  magnetic  moment  of  NS  and  2m'l  is  that  of  ns, 
hence  the  turning  moment  reduces  to 

2M.M' 

If,  in  accordance  with  what  we  have  assumed  above,  ns  be  very 
small  in  comparison  to  Z),  the  field  about  ns  is  uniform,  and  if  ns 
be  deflected  through  an  angle  5,  the  turning  moment  becomes 

2M.M' 


150.  Measurement  of  Strength  of  Magnetic  Field.  —  From 
Par.  130  we  have  seen  that  if  a  needle  of  magnetic  moment  M'  be 
placed  in  a  field  of  strength  H  and  be  deflected  through  an  angle 
5,  the  moment  which  tends  to  restore  it  to  the  meridian  is 

M'.H.sind 


MAGNETISM.  117 

and  from  the  preceding  paragraph  we  have  seen  that  when  such  a 
needle,  ns,  and  a  magnet,  NS,  are  placed  in  the  relative  positions 


N 


Fig.  75. 

as  shown  in  Fig.  75,  the  turning  moment  due  to  the  magnet  is 

2M.M' 


When  equilibrium  is  reached  these  two  moments  are  equal, 
hence  —  yp  —  .  cos  5  =  M'  .  H  .  sin  5 

hence  -jj  =  -FT  •  tan  5 

D  and  5  may  be  measured  directly  and  we  thus  obtain  a  second 
expression  involving  M  and  H,  which,  when  combined  with  the 
expression  deduced  in  Par.  148,  enables  us  to  determine  H. 

The  needle  ns  being  very  small,  a  graduated  circle  over  which 
its  ends  might  travel  could  not  be  read  with  much  accuracy,  there- 
fore, the  angle  6  is  usually  determined  by  observing  the  movement 
over  a  scale  of  a  beam  of  light  reflected  from  a  tiny  mirror  attached 
to  the  needle.  This  method  of  reading  the  deflection  of  a  needle 
will  be  more  fully  explained  in  the  description  of  the  mirror  gal- 
vanometer (Par.  377). 


118  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  15. 
THEORY   OF   MAGNETISM. 

151.  Magnetism. — As  in  the  case  of  electricity,  we  must  at  the 
outset  admit  that  we  do  not  know  what  magnetism  is.    It  is  not 
matter  yet  in  its  manifestations  it  must  always  be  associated  with 
matter.    Gilbert  called  attention  to  the  fact  that  with  one  magnet 
we  could  make  hundreds  of  others  and  yet  the  strength  and  weight 
of  the  original  magnet  would  be  unaltered.    We  can  conceive  of 
no  form  of  matter  which  could  thus  be  dipped  out  or  drawn  from 
indefinitely  and  yet  the  original  source  of  supply  be  undiminished. 
It  is  not  electricity.    A  charged  body  placed  in  a  magnetic  field 
is  not  on  account  of  its  charge  acted  upon  in  any  different  way,  nor 
is  a  magnetized  body  placed  in  an  electric  field  attracted  or  re- 
pelled in  any  different  manner  on  account  of  its  magnetism.    An 
electric  current  does  however  produce  certain  magnetic  effects, 
and  mechanical  energy  expended  in  moving  or  varying  magnetic 
fields  may  be  transmuted  into  electric  energy.    We  may  say  then 
that  with  electric  currents  we  can  produce  magnetism  and  from 
magnetism  we  can  produce  electric  currents. 

Magnetic  forces  pass  with  equal  ease  through  the  hardest  sub- 
stances, the  thinnest  gases  and  a  vacuum.  The  medium  concerned 
in  this  propagation  is  therefore  considered  to  be  the  ether. 

152.  Molecular  Magnetism. — We  have  already  seen  (Par.  Ill) 
that  if  a  bar  magnet  be  broken  across,  one  surface  of  this  fracture 
will  be  of  north  polarity,  the  other  of  south,  and  this  no  matter  at 
what  point  the  bar  be  broken  nor  how  the  line  of  fracture  runs 
across.    If  these  portions  be  again  broken,  the  resulting  fragments 
will  still  possess  polarity  and  even  if  the  final  result  be  dust  the 
ultimate  particles  will  still  be  little  magnets.    The  inevitable  con- 
clusion is  that  the  individual  molecules  are  themselves  magnets 
and  that  they  are  arranged  with  their  like  poles  all  pointing  in  one 
direction.    This  affords  a  satisfactory  explanation  of  the  fact  that 
the  free  magnetism  resides  mainly  at  the  poles,  for  at  any  inter- 
mediate cross-section  the  magnetism  on  one  side  of  the  section  is 


MAGNETISM.  119 

exactly  balanced  and  neutralized  by  that  on  the  other,  consequent- 
ly, the  end  layers  are  the  only  ones  free  to  cause  external  effect. 

153.  Ewing's  Theory. — Two  hypotheses  may  be  advanced  to 
account  for  the  arrangement  of  the  molecular  magnets.     First, 
before  a  steel  bar  is  magnetized  its  molecules  are  unmagnetized 
and  the  act  of  magnetizing  imparts  to  them  their  magnetism  and 
arrangement.    This  throws  but  little  light  on  the  matter.    Second, 
the  molecules  possess  magnetism  as  an  inherent  property  and  are 
always  magnetized  but  are  indiscriminately  arranged  or  rather 
are  arranged  in  little  groups  satisfying  each  other's  polarity  and 
thus  neutralizing  each  other's  magnetic  effects  and  producing 
little  or  no  external  magnetism.    The  act  of  magnetizing  simply 
turns  these  molecules  until  their  like  poles  point  in  one  direction. 
The  maximum  effect  would  be  produced  when  all  of  the  molecules 
had  been  turned  and  the  magnet  is  then  said  to  be  saturated. 

This  theory  was  first  advanced  by  Weber  and  later  elaborated 
by  Ewing,  whose  name  it  bears.  The  latter  showed  that  it  satis- 
factorily accounts  for  the  known  facts  of  magnetization,  especially, 
as  will  be  seen  later  (Par.  395),  for  the  varying  rate  of  change  of 
magnetism  accompanying  a  constant  rate  of  change  of  the  mag- 
netizing force.  Certain  corroborating  phenomena  are  described 
in  the  following  paragraphs. 

154.  Magnetization  is  Accompanied  by  Molecular  Movement. 

(a)  If  a  small  glass  tube  be  filled  with  steel  filings  and  then 
subjected  to  magnetization,  the  filings  will  be  seen  to  arrange 
themselves  .-end  to  end  and  thereafter  the  tube  will  act  as  a  magnet. 
This  is  thought  to  be  analogous  to  what  takes  place  among  the 
molecules  of  a  magnetic  body  during  magnetization.    If  the  filings 
be  shaken  up  and  disarranged  the  magnetism  disappears. 

(b)  When  an  iron  bar  is  suddenly  magnetized  by  an  electric 
current  a  metallic  clink  is  heard.    This  could  be  produced  only 
by  a  vibration  among  the  molecules  of  the  bar. 

(c)  When  an  iron  bar  is  rapidly  magnetized  and  demagnetized 
it  grows  hot.    This  heat  could  be  produced  only  by  internal  move- 
ment among  the  molecules. 

(d)  Magnetization  is  accompanied  by  a  change  in  the  dimen- 
sions of  the  magnetic  substance.    An  iron  bar  strongly  magnetized 
increases  1/720,000  of  its  length  but  if  still  more  strongly  magnet- 
ized it  contracts  again.    A  bar  of  cobalt  at  first  diminishes  and 


120  ELEMENTS  OF  ELECTRICITY. 

then  increases.  Nickel  diminishes  from  the  first.  Later  inves- 
tigations show  that  iron  and  steel  contract  along  the  lines  of 
magnetization  and  expand  across  these  lines.  The  change  in 
dimensions  must  result  from  movement  among  the  molecules. 

155.  Freedom  of  Molecular  Movement  Facilitates  Magneti- 
zation.— When  a  magnetic  body  is  placed  in  a  magnetic  field,  we 
may  consider  that  a  force  is  tugging  at  each  of  the  little  molecular 
magnets  endeavoring  to  turn  them  so  that  their  like  poles  will 
point  in  one  direction.    This  turning  is  impeded  by  the  crowding 
of  the  molecules  or  by  what  may  be  designated  molecular  friction. 
If  this  crowding  or  friction  be  relieved  in  any  way,  as  by  vibration, 
by  heating  or  by  liquefaction,  magnetization  is  rendered  much 
easier. 

It  has  long  been  known  that  hard  steel  is  very  much  more 
difficult  to  magnetize  than  soft  iron  but  that  once  magnetized  it 
retains  its  magnetism  much  better,  or,  as  this  last  is  usually 
expressed,  its  retentivity  is  much  greater  than  that  of  iron.  We 
may  consider  that  the  molecules  of  the  rigid  steel  offer  more 
resistance  to  turning  than  do  those  of  the  soft  iron,  and  on  account 
of  this  same  rigidity  they  remain  more  persistently  in  the  position 
into  which  they  have  been  turned.  A  piece  of  pure  iron  loses  its 
magnetism  as  soon  as  the  magnetizing  force  is  discontinued.  The 
iron  generally  used  in  electrical  machinery  is  not  absolutely  pure 
and  some  traces  of  magnetism  persist  after  the  cessation  of  the 
magnetizing  force.  This  residual  magnetism  plays  an  important 
part  in  certain  electric  machines. 

156.  Magnetization  Facilitated  by  Vibration. — Vibration,  how- 
ever produced,  is  favorable  to  loosening  up  the  molecules  of  a  body. 
Gilbert  discovered  that  if  an  iron  bar  held  in  the  magnetic  merid- 
ian be  struck  with  a  hammer  it  becomes  a  magnet,  but  no  such 
effect  is  produced  if  the  bar  be  held  crosswise. 

The  steel  columns  employed  so  largely  in  modern  buildings  are 
all  planted  in  the  meridian  and  in  accordance  with  the  principle 
stated  in  Par.  143  are  penetrated  lengthwise  by  the  lines  of  force 
of  the  earth's  field  (see  Fig.  76).  They  are  subjected  to  continual 
vibration  and  therefore  become  in  course  of  time  highly  mag- 
netized. The  lower  ends  of  all  such  columns  in  the  northern 
hemisphere,  being  the  ends  from  which  the  lines  of  force  emerge, 
are  north  poles  (Par.  142).  This  also  explains  the  fact  which 


MAGNETISM. 


121 


several  centuries  ago  caused  great  wonderment,  that  is,  that  iron 
crosses  on  church  steeples  and  the  iron  rods  of  weather  vanes  are 
often  found  to  have  acquired  magnetic  properties. 


Fig.  76. 

157.  Loss  of  Magnetization  Facilitated  by  Vibration. — Reflec- 
tion will  show  that  the  foregoing  principle  works  both  ways,  that 
is,  if  an  iron  bar  be  placed  in  the  meridian  and  jarred  it  acquires 
magnetism;  on  the  other  hand,  if  a  magnet  not  in  the  meridian 
be  jarred  it  loses  its  magnetism.    Great  care  must  then  be  observed 
in  handling  magnets  not  to  jar  them  by  striking  or  by  dropping 
or  otherwise,  as  under  such  conditions  they  deteriorate  rapidly. 
Even  if  a  magnet  be  in  the  meridian  when  jarred,  it  loses  strength 
for  the  earth's  field,  being  much  weaker  than  the  magnetic  field 
originally  used  in  making  the  magnet,  can  not  hold  in  position  all 
of  the  molecules  when  they  begin  to  vibrate. 

158.  Effect  of  Heat. — It  is  known  that  when  a  body  is  heated 
its  molecules  are  put  into  more  or  less  violent  vibration.    When  a 
magnetic  body  is  heated  to  a  red  heat  the  vibrations  reach  such  a 
pitch  that  they  are  no  longer  controlled  by  magnetic  force,  that 
is,  its  molecules  are  dancing  about  so  that  the  magnetic  force  can 
no  longer  pull  them  into  line,  therefore,  at  a  red  heat  magnets  lose 
their  magnetism  and  magnetic  bodies  are  no  longer  attracted  and 
can  no  longer  be  magnetized.    If,  however,  such  heated  bodies  be 
allowed  to  cool  in  a  magnetic  field,  the  molecules  as  they  quiet 
down  take  positions  in  accordance  with  the  magnetic  force  and  the 
result  is  that  the  bodies  acquire  magnetism.    Gilbert  found  that 
bars  of  iron  or  steel  heated  to  redness  and  allowed  to  cool  in  the 


122  ELEMENTS  OF  ELECTRICITY. 

meridian  became  magnets.  If  molten  cast-iron  be  run  into  a 
mould  and  cools  and  solidifies  in  a  strong  magnetic  field  it  acquires 
magnetism. 

159.  Magnetization  Facilitated  by  Solution.— When  a  body  is 
in  solution  it  is  separated  into  its  individual  molecules  and  these 
have  great  freedom  of  movement.  Deposition  from  solution 
must  take  place  molecule  by  molecule.  Should  a  magnetic  sub- 
stance in  solution  be  deposited  while  in  a  magnetic  field,  the 
molecules  should  have  no  trouble  in  arranging  themselves  and  the 
resulting  body,  if  our  hypothesis  be  correct,  should  exhibit  marked 
magnetic  properties.  This  has  been  confirmed  experimentally  by 
depositing  iron  electrolytically  (as  electroplating  is  done)  in  a 
strong  field. 

We  are  taught  by  geology  that  beds  of  iron  ore  are  accumulated 
through  chemical  processes  by  deposition  from  solution.  Since 
this  deposition  takes  place  in  the  earth's  magnetic  field,  this 
affords  a  reasonable  explanation  of  the  occurrence  of  the  lode- 
stone.  Gilbert,  although  he  wrote  long  before  the  atomic  theory 
had  been  advanced,  evidently  had  this  thought  in  mind  and  in 
Chapter  II,  Book  III  of  his  work  gives  the  following  significant 
experiment.  "We  once  had  chiselled  and  dug  out  of  its  vein  a 
lodestone  twenty  pounds  in  weight,  having  first  noted  and  marked 
its  extremities;  then  after  it  had  been  taken  out  of  the  earth  we 
placed  it  on  a  float  in  water  so  it  could  freely  turn  about;  straight- 
way, that  extremity  of  it  which  in  the  mine  looked  north  turned  to 
the  north  in  water  and  after  a  while  there  abode." 


MAGNETISM.  123 


CHAPTER  16. 

MANUFACTURE  OF  MAGNETS. 

160.  Most  Suitable  Metal  for  Making  Magnets. — We  have 
stated  that  soft  iron  is  far  more  easily  magnetized  than  steel  but 
on  the  other  hand  its  retentivity,  or  power  of  retaining  imparted 
magnetism,  is  very  slight.    The  best  permanent  magnets  are  made 
from  glass-hard  steel,  that  is,  steel  which  has  been  heated  to  a 
bright  red  and  then  plunged  into  cold  water.     Certain  metals 
alloyed  with  steel  improve  its  magnetic  properties  and  others 
injure  or  destroy  them.    An  alloy  of  tungsten  produces  magnets 
of  great  retentivity,  while  an  alloy  of  manganese  can  hardly  be 
magnetized  at  all  and  has  been  proposed  for  structural  work  in 
electrical  laboratories. 

161.  Principle  of  Manufacture  of  Magnets. — We  have  seen 
that  in  theory  a  bar  of  steel  becomes  a  magnet  when  its  molecules 
have  been  turned  so  that  their  poles  lie  in  one  direction.    The 
manufacture  of  magnets  is  based  upon  this  theory,  and  just  as  we 
get  the  individual  hairs  of  a  piece  of  fur  to  lie  in  one  direction  by 
combing  or  by  brushing  or  by  blowing  upon  the  fur,  so  we,  in  a 
sense,  comb  or  brush  or  blow  the  molecules  of  the  bar  of  which 
we  wish  to  make  a  magnet.    The  principle  of  these  processes  is 
the  same;  they  differ  merely  in  details  of  execution. 

162.  Magnetization  by  Single  Touch. — In  this  method  the  bar 
to  be  magnetized  is  placed  horizontal  and  preferably  with  its  ends 


Fig.  77. 


resting  upon  or  just  in  front  of  opposite  poles  of  two  magnets  as 
shown  in  Fig.  77.  It  may  then  be  stroked  from  end  to  end  with  a 
magnet,  using  the  pole  of  the  same  kind  as  that  near  which  the 


124  ELEMENTS  OF  ELECTRICITY. 

last  touched  end  of  the  bar  is  resting.  A  better  way  is  to  begin  at 
the  middle  of  the  bar  and  stroke  it,  the  stroking  magnet  following 
the  path  shown  by  the  dotted  line  in  the  figure,  then  reverse  ends 
of  the  stroking  magnet  and  stroke  the  other  half  of  the  bar  in  the 
opposite  direction.  Finally,  turn  the  bar  over  and  repeat  the 
strokings  upon  the  other  side.  The  point  last  touched  is  of 
opposite  polarity  to  the  pole  with  which  it  is  stroked. 

163.  Magnetization  by  Divided  Touch. — This  method  is  in 
principle  precisely  the  same  as  the  foregoing  and  differs  only  in 
that  two  magnets  are  used  in  the  strokings.  The  opposite  poles 
of  the  two  magnets  are  placed  at  the  center  of  the  bar  (Fig.  78)  and 


Fig.  78. 

are  then  drawn  apart,  the  magnets  following  the  paths  shown  by 
the  dotted  lines  in  the  figure.  After  eight  or  ten  strokes,  the  bar 
is  turned  over  and  the  other  side  is  stroked.  Sometimes  a  block 
of  wood  is  placed  between  the  poles  of  the  stroking  magnets  and 
they  are  held  against  this  and  slid  back  and  forth  along  the  bar, 
being  finally  removed  at  the  center  of  the  bar.  This  last  is  called 
the  method  by  double  touch. 

164.  Magnetization  by  an  Electric  Current. — The  best  method 
of  magnetization  is  by  means  of  an  electric  current.  An  insulated 
wire  is  coiled  around  the  bar  to  be  magnetized  and  a  current  is 


-0\ 


Fig.  79. 

sent  through  the  wire.  As  result  of  this  treatment  the  bar  be- 
comes a  magnet.  A  full  explanation  of  this  can  not  be  given 
without  anticipating  certain  principles  which  have  not  yet  been 
developed  and  it  must  therefore  be  deferred  until  later,  but  it  can 
be  stated  that  if  a  current  flows  through  the  coiled  wire  as  shown 
diagrammatically  in  Fig.  79  and  in  the  direction  of  the  small 


MAGNETISM.  125 

arrowheads,  there  will  be  produced  inside  of  the  hollow  of  the  coil  a 
magnetic  field  whose  lines  of  force  run  as  shown  by  the  large  arrow, 
that  is,  inside  of  this  hollow  space  around  which  the  coil  is  wrapped 
lines  of  force  will  run  like  a  draught  runs  up  a  chimney  and  an 
iron  or  steel  bar  placed  in  this  field  will  have  its  molecules  all 
swept  or  "blown"  into  a  common  direction,  and  in  the  case  of 
steel  a  great  part  of  them  retain  this  new  position.  They  really 
turn  in  accordance  with  the  principle  given  in  the  latter  part  of 
Par.  144. 

165.  Consequent   Poles. — If  a  magnet  be  touched  at  some 
point  between  its  poles  by  a  second  magnet,  the  molecules  around 
that  point  may  be  disarranged  to  the  extent  of  producing  poles 
intermediate  to  the  original  ones.    Such  intermediate  poles  are 
called  consequent  poles.     They  are  usually  the  result  of  some 
accident  or  error  in  the  process  of  magnetization.    Their  presence 
may  be  detected  by  exploring  the  field  about  the  magnet  by  means 
of  a  small  compass  needle  or  by  use  of  the  magnetic  figures.   They 
may  be  intentionally  produced  by  stroking  the  bar  in  a  different 
manner  from  that  prescribed  or,  in  the  electric  method,  by  wrap- 
ping a  portion  of  the  coil  in  opposite  direction  to  the  rest.    If,  for 
example,  a  steel  knitting  needle  be  stroked  with  the  north  pole  of 
a  magnet,  the  strokes  beginning  at  each  end  and  terminating  at 
the  center,  the  needle  will  be  found  to  have  a  north  pole  at  each 
end  and  a  south  pole  at  the  center. 

166.  Magnetization    Largely    Confined    to    Outer    Layers    of 
Magnet. — The  process  of  magnetization  effects  the  outer  layers 
of  the  steel  bar  more  than  it  does  the  interior  portions.    This  may 
be  shown  in  several  ways.    If  a  magnet  be  placed  in  acid  and  its 
outer  layer  be  dissolved  off,  its  magnetism  will  be  found  to  de- 
crease at  a  more  rapid  rate  than  its  mass.    Again,  if  a  number  of 
thin  flat  pieces  of  steel,  as  for  example  blades  of  table  knives,  be 
bound  up  in  a  bundle  and  magnetized,  it  will  be  found  when  the 
bundle  is  taken  apart  that  those  on  the  outside  of  the  bundle  are 
much  more  strongly  magnetized  than  those  on  the  interior.    There 
are  three  reasons  for  this.    First,  when  the  magnetism  is  imparted 
by  stroking,  the  outer  layers  act  as  a  magnetic  screen  for  the  inner 
layers  (Par.  143),  that  is,  the  teeth  of  our  magnetic  comb  do  not 
reach  down  into  the  deeper  layers  of  molecules.    Second,  when  the 
electric  method  is  used,  the  field  is  stronger  close  to  the  wire  than 


126  ELEMENTS  OF  ELECTRICITY. 

it  is  in  the  center  of  the  coil  so  the  outer  portions  of  the  bar  become 
more  highly  magnetized.  Third,  the  outer  layers  act  by  induction 
upon  the  inner  layers  and  tend  to  produce  in  them  an  opposite 
polarity,  thereby  weakening  them.  This  last  may  be  shown  as 
follows.  If  three  similar  steel  bars  be  magnetized  equally  and  then 
tied  together  and  used  as  a  magnet,  when  they  are  again  taken 
apart  the  inner  one  will  be  found  to  be  weaker  than  the  outer  ones. 
Since  thin  ribbon-like  bars  can  be  more  thoroughly  magnetized 
than  thicker  ones,  the  most  powerful  magnets  are  made  of  a 


Fig.  80. 

number  of  these  separately  magnetized  and  then  bound  together. 
Such  laminated  magnets  are  powerful  but,  for  reasons  just  explained, 
their  power  does  not  increase  in  direct  proportion  to  the  number 
of  laminae  or  strips.  It  is  found  best  to  have  the  interior  layers 
project,  as  shown  in  Fig.  80,  slightly  beyond  the  outer  layers. 
Sometimes  the  ends  of  such  magnets  are  inserted  into  soft  iron 
pole  pieces. 

167.  Aging  of  Magnets. — Even  if  they  are  handled  carefully 
and  not  jarred,  magnets  grow  weaker  with  time,  most  probably  on 
account  of  the  inductive  effect  mentioned  in  the  preceding  para- 
graph, and  may  take  several  years  to  attain  a  constant  state.  In 
certain  electrical  measuring  instruments  in  which  magnets  are 
used,  it  is  of  the  utmost  importance  that  these  retain  a  constant 
strength.  Such  magnets  can  be  put  through  an  artificial  process 
of  aging  by  which  the  constant  state  can  be  reached  quickly.  This 
treatment  consists  in  exposing  the  newly  made  magnet  to  a  current 
of  steam  for  some  20  hours,  then  remagnetizing  it  and  exposing  it 
again  to  steam  for  ten  hours. 


MAGNETISM.  127 


CHAPTER  17. 
TERRESTRIAL   MAGNETISM. 

168.  Location  of  Earth's  Magnetic  Poles. — We  have  seen  that 
Gilbert  made  the  discovery  that  the  earth  itself  is  a  magnet. 
Starting  from  this  point  we  are  naturally  led  to  enquire  where  are 
its  poles,  what  is  the  direction  and  intensity  of  its  field  at  different 
localities  and,  finally,  why  is  it  a  magnet. 

In  experimenting  with  his  spherical  lodestones  or  terrellas  Gil- 
bert located  their  poles  as  follows.  He  laid  a  short  piece  of  iron 
wire  upon  the  surface  of  the  terrella  near  its  equatorial  region. 
The  wire  became  a  magnet  by  induction  and  turning  on  the 
polished  surface  of  the  sphere,  as  if  on  a  pivot,  pointed  toward  the 
pole.  The  direction  in  which  the  wire  pointed  was  marked  with 
chalk  and  the  wire  was  then  shifted  to  some  other  position  and  its 
direction  again  marked.  These  chalk  lines  prolonged  intersected 
at  the  poles.  Were  the  earth  a  homogeneous  sphere  its  magnetic 
poles  could  probably  be  located  similarly,  that  is,  the  direction  in 
which  a  magnetic  needle  pointed  at  various  localities  could  be 
determined  and  these  direction  lines  prolonged  would  intersect 
at  the  poles,  but  the  earth  is  far  from  being  such  a  sphere  and  a 
series  of  needles  distributed  around  a  parallel  of  latitude  would 
indicate  directions  not  even  approximately  converging. 

If  we  should  start  at  any  point  with  a  magnetic  needle  and 
move  it  continually  in  the  direction  of  its  length,  just  as  is  done 
in  the  method  described  in  Par.  141,  we  would  not  trace  the  arc  of 
a  great  circle  but  a  curved  line  which  if  prolonged  in  both  direc- 
tions would  eventually  pass  through  the  magnetic  poles.  Two 
such  lines  would  by  their  intersections  locate  the  poles. 

Figure  81  represents  a  portion  of  the  northern  hemisphere  with 
a  series  of  such  curves  which  begin  at  points  along  the  equator 
ten  degrees  apart.  It  will  be  noted  that  the  north  magnetic  pole 
does  not  coincide  with  the  geographical  pole  and  is  in  fact  nearly 
twenty  degrees,  or  some  twelve  hundred  miles,  south  of  the  latter. 
It  was  discovered  by  Sir  J.  C.  Ross  during  the  arctic  expedition 
of  1829-33  and  is  located  on  the  Island  of  Boothia  Felix,  north  of 


128 


ELEMENTS  OF  ELECTRICITY. 


Hudson  Bay,  in  latitude  70°  5'  north  and  longitude  96°  43'  west. 
The  south  magnetic  pole  has  not  been  reached.  It  is  located  in  the 
antarctic  regions  in  approximately  latitude  73°  30'  south  and 
longitude  147°  30'  east,  whence  it  is  seen  that  the  two  magnetic 
poles  are  not  at  the  extremities  of  a  diameter  of  the  earth. 

It  follows  from  the  foregoing  that  what  we  have  designated  in 
the  preceding  pages  as  the  magnetic  meridian,  or  the  vertical  plane 
through  the  axis  of  the  poised  needle,  does  not  in  general  pass 
through  the  magnetic  poles  and  furthermore  changes  its  direction 
from  point  to  point. 


169.  Magnetic  Declination.— A  study  of  Fig.  81  will  show  that 
within  its  limits  there  are  three  and  only  three  regions  in  which 
the  needle  points  to  the  geographic  north  pole.  These  regions, 
marked  A,  B  and  C  on  the  map,  are  the  western  side  of  Hudson 
Bay,  the  vicinity  of  St.  Petersburg  in  Russia  and  the  eastern 
portion  of  Siberia.  At  other  points  the  needle  points  either  to  the 
east  or  to  the  west  of  the  true  meridian.  Thus,  along  a  parallel 
from  St.  Petersburg  to  Hudson  Bay  the  needle  points  to  the  west 
of  the  meridian,  while  continuing  from  Hudson  Bay  to  Siberia  it 


MAGNETISM.  129 

points  to  the  east.  This  deviation  of  the  needle  from  the  true 
meridian  is  called  the  magnetic  declination.  We  shall  see  later  that 
the  declination  at  any  locality  is  slowly  changing.  In  1905  along 
a  line  through  Charleston,  S.  C.,  Cincinnati,  Ohio,  Lansing, 
Michigan,  and  thence  across  Lake  Superior  the  needle  pointed 
true  north,  while  in  the  northeast  corner  of  Maine  the  declina- 
tion was  21°  west  and  in  the  extreme  northwest  of  the  State  of 
Washington  it  was  24°  east.  The  magnetic  declination  is  some- 
times called  the  magnetic  variation,  but  there  are  several  kinds  of 
magnetic  variation  and  the  term  declination  is  to  be  preferred. 

170.  Isogonic  Chart. — It  is  of  the  utmost  importance  that 
navigators  should  know  the  magnetic  declination  at  whatever 
point  their  vessel  may  be.    For  example,  if  a  vessel  be  off  the  mouth 
of  the  Columbia  River  and  its  captain,  wishes  to  sail  due  north, 
he  must  steer  by  compass  22°  to  the  west  of  north.    A  knowledge 
of  the  declination  is  also  required  by  surveyors.    Information  of 
this  kind  is  often  given  graphically  in  so-called  magnetic  maps. 
One  of  these,  for  the  year  1905,  is  shown  in  Fig.  82  and  is  prepared 
by  joining  by  a  continuous  line  all  those  points  at  which  in  that 
year  the  declination  was  the  same.     The  resulting  curves  are 
called  isogonic  lines  (lines  of  equal  declination)  and  the  map  is 
called  an  isogonic  chart.    The  heavy  lines  are  the  agonic  lines,  or 
lines  of  no  declination;  the  lighter  lines  are  those  of  westerly 
declination;  the  dotted  lines  are  those  of  easterly  declination.    It 
will  be  noted  that  there  is  one  agonic  line  completely  encircling 
the  earth  (shown  as  two  in  the  Mercator's  projection  used  in  the 
chart)  and  a  second  one  embracing  an  elliptical  area  in  eastern 
Asia.    This  last  is  called  the  Siberian  oval. 

Figure  83  is  the  isogonic  chart  for  the  United  States  for  the  year 
1905  taken  from  the  report  of  the  Superintendent  of  the  Coast 
Survey  for  1906. 

171.  Magnetic  Dip. — In  manufacturing  needles  for  compasses 
and  surveying  instruments,  they  are  shaped  and  finished  off  while 
the  metal  is  soft,  after  which  they  are  tempered  glass  hard  and 
then   magnetized.     They  are   carefully  balanced   before  being 
tempered  for  afterwards  they  are  too  hard  to  file  and  grinding 
would  injure  their  magnetization.    Robert  Norman,  an  instrument 
maker  of  London,  noticed  in  1576  that  no  matter  how  carefully 
he  balanced  his  needles  they  were  thrown  out  of  balance  after 


130 


ELEMENTS  OF  ELECTRICITY. 


MAGNETISM. 


131 


132  ELEMENTS  OF  ELECTRICITY. 

being  magnetized  and  invariably  the  north  end  appeared  to  be 
the  heavier  so  that  he  was  compelled  to  restore  the  balance  by 
sticking  a  small  piece  of  wax  under  the  south  end.  Being  angered 
one  day,  or  as  he  expressed  it  "being  stroken  into  some  choler," 
by  ruining  a  needle  upon  which  he  had  expended  a  good  deal  of 
labor  and  whose  balance  he  endeavored  to  restore  by  cutting  off 
a  small  piece  from  the  north  end,  he  began  to  reflect  upon  the 
matter  and  finally  made  a  needle  which,  before  being  magnetized, 
balanced  on  horizontal  trunnions.  After  magnetization,  the 
north  end  dipped  down  until  the  needle  stood  at  an  angle  of  72° 
with  the  horizontal  plane.  The  angle  which  the  axis  of  such  a 
needle  makes  with  the  horizontal  plane  is  called  the  magnetic  dip 
or  magnetic  inclination.  The  explanation  of  the  magnetic  dip  is 
as  follows:  The  lines  of  force  of  the  earth's  magnetic  field  not 
being  circles  and  its  poles  being  at  some  unknown  depth,  these 
lines  of  force  are  not  parallel  to  the  surface  but  penetrate  it,  in 
'Other  words,  they  are  inclined  to  the  plane  of  the  horizon.  A 
magnetic  needle  free  to  move  in  a  vertical  as  well  as  in  a  horizontal 
plane  will  place  itself  tangent  to  the  lines  of  force  and  the  angle 
which  these  lines  make  with  the  horizontal  plane  is  the  magnetic 
dip.  As  in  the  case  of  the  declination,  the  dip  is  slowly  changing. 

The  lack  of  balance  in  the  needles  of  engineering  instruments 
is  frequently  corrected  by  wrapping  a  fine  silver  wire  about  the 
south  end  of  the  needle. 

172.  Dipping  Needle. — A  needle  arranged  to  measure  the  angle 
of  dip  is  called  a  dipping  needle.  One  of  these  is  shown  in  Fig.  84. 
The  needle  is  ten  or  twelve  inches  long  and  is  mounted  upon  a 
steel  knife-blade  axis  resting  upon  polished  agate  bearings.  For 
still  more  delicate  observations  an  instrument  is  used  in  which  the 
needle  is  suspended  at  the  center  of  a  complete  graduated  circle 
which  may  be  rotated  about  a  vertical  axis  and  which,  like  a 
surveyor's  transit,  is  furnished  with  a  slow  motion  screw  by 
which  it  may  be  accurately  placed  in  the  meridian.  The  angles 
are  read  by  verniers  and  microscopes  and  observations  are  mul- 
tiplied so  as  to  eliminate  instrumental  errors.  For  example,  to 
correct  for  the  error  due  to  the  line  joining  the  90°  marks  at  the 
top  and  bottom  of  the  graduated  circle  not  being  vertical,  the 
angle  marked  by  the  needle  is  read,  the  circle  is  then  rotated  180° 
around  its  vertical  axis,  the  angle  is  again  read  and  the  mean  of 
these  observations  is  taken.  To  correct  for  the  error  due  to  the 


MAGNETISM. 


133 


axis  of  suspension  of  the  needle  not  corresponding  with  the  center 
of  the  circle,  both  ends  of  the  needle  are  read  and  the  mean  of  these 
readings  is  taken.  To  correct  for 
error  due  to  the  magnetic  axis  of 
the  needle  not  corresponding  with 
its  geometric  axis,  the  above  ob- 
servations are  repeated  with  the 
needle  reversed  from  back  to  front 
and  these  readings  are  combined 
with  the  former  ones.  To  correct 
for  error  due  to  lack  of  mechanical 
balance  in  the  needle,  observations 
are  made,  the  needle  is  then  de- 
magnetized and  remagnetized  in 
the  opposite  direction,  placed  in 
position,  a  second  set  of  observa- 
tions taken  and  the  means  of  the 
two  sets  combined.  There  are 
observed  other  refinements  not 
necessary  to  mention  here. 

173.  Isoclinic  Chart.— Figure  85 

represents  a  section  of  the  earth    _ 

by  a  plane  passing  through  its  axis  i?ig.  §4. 

and  the  north  magnetic  pole.   The 

arrows  represent  the  position  of  the  dipping  needle  at  the  corre- 
sponding points.    At  the  magnetic  poles  the  dip  is  90°  or  the 


Fig.  85. 

needle  stands  vertical  and  this  was  one  of  the  observations  by 
means  of  which  the  north  magnetic  pole  was  located.     Along 


134 


ELEMENTS  OF  ELECTRICITY. 


MAGNETISM.  135 

the  magnetic  equator,  which  in  the  western  hemisphere  lies  south 
of  the  geographical  equator,  the  dip  is  zero  or  the  needle  lies 
horizontal.  Lines  connecting  those  points  on  the  earth's  surface 
where  the  dip  is  the  same  are  called  isoclinic  lines.  An  examina- 
tion of  the  isoclinic  chart,  Fig.  86,  will  show  that  these  lines 
run  generally  east  and  west  but  curve  irregularly  and  are  not 
parallel. 

174.  Magnetic  Intensity. — The  strength  of  the  earth's  field, 
or  the  magnetic  intensity,  can  not  easily  be  measured  directly  but 
by  the  method  outlined  in  Pars.  148,  149  and  150  we  may  deter- 
mine its  horizontal  component,  whence,  since  the  total  intensity 
is  equal  to  this  horizontal  component  divided  by  the  cosine  of  the 
angle  of  dip,  the  total  intensity  is  readily  calculated. 

Having  determined  the  horizontal  component  at  one  point,  it 
may  easily  be  determined  at  any  other  by  applying  the  method 
by  oscillations  as  described  in  Par.  129.  The  same  magnetic  needle 
is  oscillated  for  the  same  period  of  time  at  the  two  places  and  the 
number  of  oscillations  counted;  the  horizontal  components  at  the 
two  places  are  to  each  other  as  the  square  of  the  number  of  oscil- 
lations executed  in  equal  intervals  of  time. 

The  horizontal  component  is  greatest  along  the  magnetic  equa- 
tor but  varies  at  different  points  along  this  line.  It  is  a  maximum 
over  a  region  embracing  a  part  of  India,  the  Malay  Peninsula 
and  the  Islands  of  Borneo  and  New  Guinea,  its  strength  being 
.38,  that  is,  a  unit  pole  placed  in  the  earth's  field  in  this  region 
would  be  urged  in  a  horizontal  direction  with  a  force  of  .38  dynes. 
At  the  magnetic  poles  the  horizontal  component  is  zero  and  near 
these  points  the  total  intensity  is  determined  from  the  vertical 
component  instead  of  from  the  horizontal.  The  total  intensity 
increases  from  the  equator  towards  the  magnetic  poles.  It  is 
however  not  a  maximum  at  these  poles  but  in  each  hemisphere  at 
two  points  or  magnetic  foci.  In  the  northern  hemisphere  one  of 
these  points  is  just  south  of  Hudson  Bay,  the  other  is  in  north 
central  Siberia.  In  the  southern  hemisphere  both  points  are  to 
the  south  of  Australia.  The  maximum  value  in  the  northern 
hemisphere  is  about  .65  and  in  the  southern  about  .70.  Just  as 
with  the  declination  and  the  dip,  the  total  intensity  is  found  to  be 
slowly  changing. 

Lines  connecting  points  of  equal  horizontal  intensity  or  of  equal 
total  intensity  are  called  isodynamic  lines,  and  isodynamic  charts 


136 


ELEMENTS  OF  ELECTRICITY. 


are  prepared  in  a  similar  manner  to  the  isogonic  and  isoclinic 
charts. 

175.  Magnetic  Elements. — The  declination,  the  dip  and  the 
magnetic  intensity  at  any  given  point  are  termed  the  magnetic 
elements  of  that  point.  As  observations  are  multiplied,  our  knowl- 
edge of  these  elements  and  of  the  laws  of  their  variation  corre- 
spondingly increases.  In  the  report  of  the  Superintendent  of  the 
Coast  and  Geodetic  Survey  for  1906,  data  is  presented  from  ac- 
curate observations  at  3500  stations,  or  from  every  30  miles 
square  of  the  U.  S.  territory.  The  following  table,  extracted  from 
this  report,  gives  the  declination,  dip  and  horizontal  intensity  at 
various  localities  as  determined  by  observations  made  in  the  year 
ending  June  30,  1906. 


TABLE  OF  MAGNETIC  ELEMENTS. 
1905-1906. 


Locality  Declination 

Albany,  N.  Y 11°  08'  W 

Ann  Arbor,  Mich 2°  01'  W 

Baltimore,  Md 5°  55'  W 

Bangor,  Me 17°  28' W 

Columbia,  S.C Oc 

Fargo,  N.  D llc 

Galveston,  Tex T 

Green  River,  Utah 15C 

Helena,  Mont 19C 

Honolulu 10°35'E 

Joliet,  111 2°52'E 

Key  West,  Fla 2°  31'  E 

Los  Angeles,  Cal 15C 

Memphis,  Tenn 5C 

Montreal,  Can 14< 

New  York,  N.  Y 9< 

Philadelphia,  Pa T 

Portland,  Ore 22C 

San  Francisco,  Cal 17° 

Silver  City,  N.  M 12° 

Sitka,  Alaska 30°  01'  E 

Washington,  D.  C 4°  34'  W 


0' 

30'  E 

28' E 

:o  40'  E 

49'  E 


:o  14'  E 
:o  30'  E 
40' W 
08' W 
ro  45'  W 
44' E 
00' E 
46' E 


Dip 

73°  50' 
72°  51' 
70°  42' 
74°  50' 
65°  35' 
75°  35' 
58°  37' 
66°  08' 
72°  08' 
39°  20' 
72°  13' 
55°  03' 
59°  31' 
65°  47' 
75°  38' 
72°  02' 
71°  04' 
68°  39' 
62°  43' 
59°  51' 
74°  42' 
70°  28' 


Hor.  Intensity 

.16939 
.18248 
.19560 
.15715 
.23791 
.15731 
.28404 
.23476 
.18548 
.29566 
.18857 
.29404 
.26902 
.24080 
.15122 
.18690 
.19361 
.21754 
.24898 
.27301 
.15494 
.20022 


MAGNETISM. 


137 


176.  Variation    of   the    Magnetic    Elements. — The    magnetic 
elements  at  any  locality  are  far  from  being  constant.    They  pass 
through  cycles  of  variation  with  periods  of  years,  through  others 
with  the  seasons,  still  others  in  each  twenty-four  hours  and  finally 
others  at  irregular  intervals.    These  variations  may  therefore  be 
classed  as  periodic  and  irregular,  the  first  class  embracing  the 
secular,  the  annual  and  the  diurnal  variations.    Although  all  of 
the  elements  vary,  it  is  only  to  the  variation  in  declination,  and 
furthermore  only  to  the  secular  variation  of  this  element,  that 
any  practical  importance  attaches. 

177.  Secular  Change  in  Declination  and  Dip. — For  over  300 
years  it  has  been  noted  that  the  decimation  and  dip  were  slowly 
changing.    In  1580  at  London  the  declination  was  11°  17'  east  and 
was  decreasing  so  that  in  1657  the  needle  pointed  true  north.  The 


1500 


1600 


1700 


1800 


1900 


2000 


variation  west 
20°  10° 


variation  east 
10°          20° 


Fig.  87. 


movement  continued  in  the  same  direction  until  in  1816  a  maxi- 
mum westerly  declination  of  24°  30'  was  reached  and  retrogression 
began.  In  1900  the  declination  was  16°  16'  west.  This  movement 
is  shown  graphically  by  the  curve  in  Fig.  87.  In  about  the  year 
1976,  or  some  320  years  since  the  needle  last  pointed  true  north,  it 
should  again  point  north,  but  since  the  curve  shows  that  the 


138  ELEMENTS  OF  ELECTRICITY. 

westerly  variation  is  greater  than  the  easterly,  the  period  of  a 
complete  cycle  will  not  be  known  until  the  needle  moving  westward 
again  points  to  11°  17'  as  in  1580. 

The  change  in  declination  is  accompanied  by  a  change  in  dip, 
although  the  angular  range  of  the  dip  is  much  less  than  that  of  the 
declination.  At  London  the  total  variation  in  dip  has  been  7°  33' 
while  that  in  declination  has  been  35°  47';  however,  the  range  in 
dip  is  still  increasing  which  is  not  true  of  the  range  in  declination. 
To  the  eye  of  the  observer  placed  at  the  pivot  of  the  needle  in 
London,  the  north  pole  of  the  needle  would  appear  to  have  traced 
in  a  clockwise  direction  since  1580  about  two-thirds  of  a  more  or 
less  irregular  and  flattened  oval.  This  fact,  taken  alone,  would 
seem  to  indicate  that  the  north  magnetic  pole  viewed  from  some 
point  outside  of  the  earth  is  slowly  rotating  hi  a  counter-clockwise 
direction  around  some  undetermined  point  in  the  northern  regions. 

As  we  travel  around  a  parallel  of  latitude  we  find,  as  has  already 
been  shown,  that  the  declination  differs  at  different  points  and  is 
changing.  We  also  find  that  both  the  direction  of  change  and  the 
rate  of  change  vary  from  place  to  place.  Thus  (Fig.  83)  across 
the  northeast  of  Maine  in  1905  the  declination  was  20°  west  and 
was  increasing  4'  per  year;  along  the  agonic  line  through  South 
Carolina  the  declination  was  varying  westerly  2'  per  year;  along 
a  line  through  Alabama,  Illinois  and  Wisconsin  the  declination 
was  stationary;  along  the  Mississippi  Valley  it  was  increasing 
easterly  V  per  year;  along  the  crest  of  the  Rocky  Mountains  it 
was  increasing  easterly  3'  per  year  and  on  the  coast  of  Oregon, 
where  the  declination  was  20°  east,  it  was  increasing  easterly  4' 
per  year.  These  changes  indicated  that  the  isogonic  lines  were 
slowly  crowding  in  upon  the  agonic  line  and  that  the  north  mag- 
netic pole  was  moving  southward.  As  observations  increase  we 
may  be  able  in  time  to  speak  with  more  certainty  of  these  move- 
ments. 

178.  Diurnal  Change  in  Declination. — The  magnetic  elements 
are  subject  to  slight  daily  changes  and  these  changes  are  more 
satisfactorily  studied  by  means  of  self  recording  instruments. 
For  instance,  a  needle  suspended  by  a  delicate  silk  fibre  carries  a 
small  concave  mirror  upon  which  falls  a  beam  of  light  from  an 
electric  bulb.  This  mirror  reflects  a  brilliant  spot  upon  a  roll  of 
photographic  paper  which  is  unwound  at  a  known  rate  by  clock- 
work. As  long  as  the  needle  is  motionless,  the  trace  of  the  spot 


MAGNETISM. 


139 


upon  the  sensitized  paper  is  a  straight  line  but  any  movement  of 
the  needle  produces  a  curve.  Fig.  88  represents  such  a  record 
made  near  London  in  1900.  At  8  A.  M.  the  declination  was  least 
but  increased  steadily  until  about  2  P.  M.  when  it  reached  a 
maximum.  It  then  decreased  until  8  P.  M.  when  it  was  nearly 
stationary  for  about  an  hour  and  then  began  to  decrease  again 
and  continued  until  8  A.  M.  A  similar  record  would  be  made  at 
all  points,  no  matter  whether  the  local  declination  be  east  or  west, 
but  the  direction  of  movement  in  the  southern  hemisphere  is  the 
reverse  of  that  in  the  northern.  Along  the  equator  the  daily 


12 


P.M. 


A.M 


PH: 


P.M. 


Fig.  88. 


range  of  the  needle  does  not  exceed  4'  while  in  northern  Europe 
it  reaches  15'. 

The  dip,  registered  in  a  similar  manner,  is  found  to  be  about  5' 
greater  in  the  morning  than  in  the  afternoon. 

179.  Annual  Change  in  Declination.  —  If  the  average  declination 
for  each  month  be  obtained  from  the  self -registering  instruments 
and  these  monthly  averages  be  compared  among  themselves,  it 
will  be  seen  that  in  the  northern  hemisphere  the  needle  moves  to 
the  west  from  May  to  September  and  to  the  east  from  September 
to  May.     In  the  southern  hemisphere  these  movements  are  re- 
versed and  in  either  case  they  are  but  slight. 

180.  Magnetic  Storms.— It  has  long  been  known  that  in  addi- 
tion to  the  periodic  variations  described  in  the  preceding  para- 


140 


ELEMENTS  OF  ELECTRICITY. 


graphs,  magnetic  needles  are  not  infrequently  subject  to  other 
variations  occurring  at  irregular  intervals.  If  a  needle  be  observed 
at  such  a  time  it  will  be  seen  to  waver  or  tremble  and  to  fluctuate 
through  an  angle  varying  from  a  few  minutes  to  one  degree  and  in 
extreme  cases  even  to  two  to  three  degrees.  The  variation  is  only 
momentary  but  may  be  often  repeated.  Such  disturbances  are 
called  magnetic  storms.  They  occur  simultaneously  at  the  most 
distant  points  and  involve  all  the  magnetic  elements.  Their 
effects  are  best  studied  by  means  of  the  curves  traced  as  described 
in  Par.  178.  The  record  instead  of  being  the  sinuous  curve  as  in 
Fig.  88  is  jagged  and  irregular.  These  storms  occur  more  fre- 
quently at  night  than  during  the  day  and  are  also  more  frequent 
in  summer  than  in  winter.  They  are  especially  marked  during 
auroral  displays  and  it  was  for  a  time  thought  that  the  two  phe- 
nomena were  related  as  effect  and  cause,  but  it  is  now  held  that 
they  have  a  common  cause. 


1810  1820  1830  1840  1850  18.60  1870  J8fcO 

Fig.  89. 

In  1852  it  was  observed  that  the  periods  of  maximum  frequency 
of  magnetic  storms  coincides  with  the  maximum  occurrence  of 
sun  spots,  both  taking  place  every  eleventh  year.  This  coin- 
cidence is  shown  graphically  in  Fig.  89  in  which  the  full  line  shows 
the  relative  number  of  sun  spots  for  each  year  and  the  broken  line 
the  number  of  magnetic  storms.  The  agreement  is  too  close  to  be 
accidental. 

181.  Theories  of  the  Earth's  Magnetism. — There  is  no  accepted 
theory  of  the  earth's  magnetism  but  since,  as  we  have  seen  above, 
its  manifestations  are  periodic  in  character,  these  periods  corre- 
sponding to  the  diurnal  and  annual  time  periods  of  the  earth  and 


MAGNETISM.  141 

to  the  eleven  year  period  of  the  sun  spots,  the  indications  are  that 
its  source  is  the  sun.  The  significance  of  the  declination  period 
has  not  yet  been  grasped,  in  fact,  as  was  pointed  out  (Par.  177), 
we  can  not  be  sure  for  a  number  of  years  to  come  what  is  the 
exact  length  of  this  period.  Could  it  be  shown  that  electric  cur- 
rents flowed  around  the  globe  from  east  to  west,  this,  as  will  be 
seen  in  electro-magnetics,  would  account  for  the  magnetic  phe- 
nomena and  this  explanation  was  advanced  and  elaborated  by 
Ampere.  So-called  earth  currents  are  known  to  exist  but  their 
direction  is  along  the  meridian  instead  of  across  it.  It  is  known 
that  electricity  is  produced  both  by  heat  and  by  evaporation,  also 
that  the  magnetic  properties  of  bodies  are  effected  by  heat,  and  it 
is  conceivable  that  the  sun  as  in  its  apparent  motion  it  sweeps 
along  overhead  at  the  equator  at  the  rate  of  1000  miles  per  hour 
may  produce  successive  masses  of  charged  vapor  which  might 
have  an  effect  similar  to  a  current,  and  also  that  the  warming  of 
successive  portions  of  the  earth's  crust  may  alter  its  magnetic 
properties  sufficiently  to  account  for  the  diurnal  and  seasonal 
variations.  An  additional  fact  which  points  to  this  hypothesis  is 
that  the  isothermal  lines,  or  lines  of  equal  average  temperature  of 
the  earth's  surface,  correspond  closely  in  direction  with  the 
isoclinal  lines. 

Faraday,  in  investigating  paramagnetic  and  diamagnetic  bodies, 
discovered  that  oxygen  is  magnetic  and  that  its  magnetism  in- 
creases as  it  grows  colder.  He  therefore  suggested  that  the  oxygen 
of  the  atmosphere  is  naturally  magnetic  and  that  the  variations 
produced  in  its  magnetism  by  the  daily  and  seasonal  variations 
in  temperature  would  afford  a  satisfactory  explanation  of  the 
periodic  variations  of  the  needle. 

Other  theories  have  been  advanced  but  they  can  not  be  regarded 
as  much  more  than  speculations. 

182.  The  Mariner's  Compass. — In  the  surveyor's  compass,  a 
long,  slender  needle  is  pivoted  free  to  rotate  within  a  horizontal 
circle  which  is  so  graduated  that  the  north  end  of  the  needle  points 
to  the  angle  which  the  line  of  sight  of  the  telescope  makes  with  the 
magnetic  meridian.  Since  the  graduated  circle  and  the  telescope 
rotate  together  about  the  vertical  axis  of  the  instrument,  the 
needle  remaining  motionless,  the  west  half  of  the  circle  must  be 
marked  east  and  the  east  half  must  be  marked  west. 


142  ELEMENTS  OF  ELECTRICITY.  } 

The  mariner's  compass  (Fig.  90)  is  differently  arranged,  the 
graduated  scale  being  fastened  to  the  needle  and  rotating  with  it 
and  hence  the  interchange  of  east  and  west  not  being  necessary. 
The  pointer  which  indicates  the  direction  in  which  the  vessel  is 


Fig.  90. 

sailing  is  a  vertical  mark  on  the  inside  of  the  box  in  which  the 
compass  turns.  In  the  compass  perfected  by  Lord  Kelvin  there 
turns  upon  an  iridium  needle  point  a  central  jewelled  cup  to  which 
is  attached  by  tightly  drawn  silk  threads  a  thin  aluminum  ring, 
six  or  eight  inches  in  diameter,  the  whole  resembling  a  wheel  of 
which  the  cup  is  the  hub  and  the  threads  the  spokes.  Upon  the 
rim  is  fastened  the  paper  scale  divided  into  the  customary  32 
"points  of  the  compass,"  and  also  with  an  outer  graduation  in 
degrees.  The  needle  proper  consists  of  eight  separate  needles, 
slender  bars  about  three  inches  long,  arranged  like  the  rungs  of  a 
ladder  and  fastened  to  the  under  side  of  the  silk  spokes,  being 
symmetrically  placed  with  respect  to  the  jewelled  cup.  The  com- 
pass is  contained  in  a  glass-covered,  cylindrical  copper  box, 
weighted  at  the  bottom  and  supported  on  gimbals.  To  the  box 
itself  there  are  attached  two  trunnions  which  rest  upon  a  copper 
ring  concentric  with  the  box.  This  ring  in  turn  carries  two  trun- 
nions which  are  in  the  same  horizontal  plane  as  the  first  pair  and 
at  right  angles  to  them,  and  these  in  their  turn  rest  upon  a  second 
and  outer  concentric  ring.  By  this  arrangement  the  compass  is 
kept  horizontal  no  matter  how  much  the  ship  may  roll.  In  order 
to  slow  down  the  oscillations  of  the  needle,  the  box  is  often  filled 
with  some  thick  non-freezing  liquid,  such  as  glycerine,  and  by 
making  a  portion  of  the  rim  of  the  compass  card  hollow,  the  liquid 


MAGNETISM.  143 

will  buoy  up  the  card  and  relieve  the  pivot  of  a  portion  of  the 
weight  upon  it. 

The  compass  and  its  box  are  placed  upon  a  pedestal,  called  the 
binnacle,  which  carries  the  necessary  lamps  for  reading  the  com- 
pass at  night  and  also  supports  the  magnets  and  masses  of  soft 
iron  used  in  making  correction  for  local  disturbances  of  the  needle. 

183.  Adjustment  of  Mariner's  Compass. — In  the  construction 
of  vessels  the  use  of  iron  and  steel  has  largely  displaced  wood. 
During  the  building  of  a  vessel  it  rests  for  a  relatively  long  period 
of  time  at  a  constant  angle  with  the  earth's  field  and  the  continual 
hammering  and  vibration  to  which  it  is  subjected  converts  it  as  a 
whole  into  a  magnet.  In  addition  to  this,  such  vertical  columns  of 
steel  as  the  cut  water  and  the  stern  post  become,  as  explained  in 
Par.  156,  magnets  whose  south  poles,  for  vessels  in  the  northern 
hemisphere,  are  at  the  upper  ends  and  therefore  about  on  a  level 
with  the  deck  upon  which  the  compass  stands.  When  such  a 
vessel  is  launched  the"  magnetism  of  the  hull  may  entirely  vitiate 
the  indications  of  the  compass.  However,  it  has  been  found  that 
by  means  of  permanent  magnets  and  of  masses  of  iron,  properly 
placed,  compensation  may  be  made  for  these  disturbing  influences. 
For  example,  reflection  will  show  that  a  magnetic  cut  water  and 
stern  post  produce  no  variation  in  the  compass  when  the  vessel 
is  sailing  in  the  magnetic  meridian,  either  north  or  south,  but  if  it 
be  sailing  in  any  other  direction  in  the  semicircles  to  the  east  or 
west,  the  compass  will  be  affected.  Since  the  error  produced  is  in 
one  semicircle  always  to  the  east  and  in  the  other  always  to  the 
west,  the  disturbance  is  called  the  semicircular  variation.  It  may 
be  corrected  by  a  vertical  rod  of  iron  or  a  sphere  of  soft  iron  placed 
on  the  opposite  side  of  the  binnacle  from  the  vertical  magnetic 
body  whose  influence  is  the  stronger.  Similarly,  the  magnetism 
of  the  hull  may  be  divided  into  two  components,  one  lengthwise  of 
the  ship,  the  other  crosswise,  and  these  can  be  separately  counter- 
balanced by  compensating  magnets  placed  usually  in  the  pedestal 
of  the  binnacle.  In  making  these  adjustments,  the  newly  launched 
vessel  is  anchored  in  some  known  position  with  reference  to  the 
magnetic  meridian  and  the  needle  is  brought  to  its  correct  reading. 
The  vessel  is  then  swung  through  an  angle  of  90°  and  adjustments 
again  made,  and  so  on  around  the  circle,  the  process  being  called 
swinging  ship.  Magnetic  masses  in  the  cargo  may  cause  disturb- 
ances of  the  needle  and  the  magnetism  of  the  hull  grows  less  with 


144  ELEMENTS  OF  ELECTRICITY. 

age  and  varies  with  the  latitude,  the  vertical  component  becoming 
entirely  reversed  when  the  magnetic  equator  is  crossed,  therefore 
the  navigator  checks  the  indications  of  his  needle  by  frequent 
astronomical  observations  and  makes  the  necessary  adjustments 
when  the  error  becomes  excessive. 

184.  Magnetism  to  be  Reverted  to  Later. — The  subject  of 
magnetism  is  usually  treated  more  extensively  than  in  the  pre- 
ceding chapters.  Thus,  a  theory  of  magnetic  potential  may  be 
developed  similarly  to  that  of  electric  potential.  It  is  thought, 
however,  that  enough  of  the  principles  have  been  given  to  enable 
the  student  to  follow  without  difficulty  the  explanations  in  the 
following  sections.  Moreover,  in  view  of  the  fact  that  electro- 
magnets, or  magnets  produced  temporarily  by  means  of  the 
electric  current,  are  for  most  purposes  far  more  suitable  and  more 
largely  used  than  permanent  magnets,  and  that  the  phenomena 
and  properties  of  the  magnetic  circuit  are  most  markedly  exhibited 
and  can  be  most  clearly  explained  by  reference  to  these  electro- 
magnets, it  is  logical  that  we  should  first  take  up  the  subject  of 
electric  currents.  Further  consideration  of  magnetism  is  there- 
fore postponed  for  the  present.  (See  Chapters  31  and  32.) 


VOLTAIC  ELECTRICITY.  145 


PART  III. 
VOLTAIC   ELECTRICITY. 


CHAPTER  18. 

DISCOVERIES   OF   GALVANI   AND   VOLTA. 

185.  Galvani's  Discovery. — The  discovery  of  current  electricity, 
or  rather  of  methods  of  producing  it  by  chemical  means,  is  as- 
cribed to  two  Italians,  Galvani  and  Volta,  the  former  Professor  of 
Anatomy  at  Bologna,  the  latter  Professor  of  Natural  Philosophy 
at  Pavia. 

Tradition  has  it  that  about  1786  the  wife  of  Galvani  being  indis- 
posed, her  physician  prescribed  for  her  a  broth  of  frogs'  legs. 
Some  had  been  procured  and  skinned  preparatory  to  cooking  and 
lay  upon  a  table  near  an  electrical  machine.  Galvani's  assistant 
happening  to  draw  a  spark  from  the  machine,  Madame  Galvani 
noticed  that  at  the  same  instant  the  severed  legs  twitched  convul- 
sively and  that  this  was  repeated  with  every  spark.  She  called  the 
attention  of  her  husband  to  this  phenomenon  which  he  imme- 
diately proceeded  to  investigate.  We  now  know  that  these  twitch- 
ings  were  produced  by  the  escape  of  the  charge  induced  in  the 
legs,  which  charge  was  released  whenever  the  machine  sparked, 
but  Galvani,  who  was  an  anatomist  and  not  an  electrician,  thought 
that  he  was  on  the  verge  of  discovering  the  vital  principle  and 
continued  his  researches  with  this  idea  in  mind.  Having  one  day 
prepared  several  pairs  of  legs  for  experiment  and  wishing  to  place 
them  to  one  side  until  they  were  needed,  he  hooked  a  copper  wire 
through  the  remnant  of  the  back  bone  and  hung  the  legs  to  the 
iron  railing  of  the  balcony  in  front  of  his  window.  A  light  wind 
was  blowing  and  to  his  astonishment  he  saw  that  whenever  the 
dangling  legs  came  in  contact  with  the  railing  they  were  thrown 
into  convulsive  movement.  Further  experiment  showed  him  that 
in  order  to  produce  these  movements  it  was  necessary  to  have  two 


146 


ELEMENTS  OF  ELECTRICITY. 


dissimilar  metals  in  contact  and  that  the  greatest  effect  was  pro- 
duced when  the  free  end  of  one  touched  a  nerve  at  the  same  time 
that  the  free  end  of  the  other  touched  a  muscle.  He  attributed 
these  effects  to  a  so-called  "animal  electricity"  whose  seat  lay  at 
the  junction  of  the  nerve  and  muscle,  where,  by  some  unknown 
vital  principle,  the  nerve  became  charged  positively  and  the 
muscle  negatively,  and,  like  the  Leyden  jar,  were  discharged  when 
connected  by  the  metals.  He  did  not  explain  why  two  metals 
were  required. 

186.  Volta's  Investigations. — Volta  was  not  long  in  hearing  of 
these  experiments  and,  favored  by  his  greater  familiarity  with 
what  was  then  known  of  electricity,  pursued  a  line  of  investigation 
which  soon  satisfied  him  that  the  true  seat  of  development  of  the 
electricity  was  not  at  the  junction  of  the  muscle  and  the  nerve 
but  at  the  point  of  contact  of  the  two  metals.  He  found  that  if 
two  dissimilar  metals  are  brought  together,  one  becomes  positively 
charged,  the  other  negatively,  that  is,  they  become  of  different 
potentials.  This  electrification  by  contact  may  be  shown  as  fol- 
lows. In  Fig.  91,  A  is  a  light  flat  needle  suspended  symmetrically 
above  the  gap  between  the  semicircular  plates  of  zinc  and  copper 
and  free  to  turn  about  the  vertical  axis  X.  If  a  positive  charge  be 
given  to  A  and  if  then  the  copper  and  zinc  plates  be  brought  into 
contact  at  B,  either  by  touching  them  together  directly  or  by 


Fig.  91. 


laying  a  piece  of  wire  across  the  gap,  the  needle  will  swing  away 
from  the  zinc  and  place  itself  above  the  copper,  thus  apparently 
showing  the  zinc  to  be  positively  charged  or  at  a  higher  potential 
than  the  copper.  Had  the  needle  been  charged  negatively,  it 
would  have  swung  away  from  the  copper  and  placed  itself  above 
the  zinc. 


VOLTAIC  ELECTRICITY.  147 

187.  Volta's  Contact  Series. — Further  investigation  by  Volta 
showed  that  for  a  given  pair  of  metals  at  a  constant  temperature, 
this  contact  difference  of  potential  is  constant  and  is  independent 
of  the  size  of  the  pieces,  of  the  amount  of  surface  in  contact  and 
of  the  length  of  time  that  they  remain  in  contact.  For  different 
pairs  of  metals,  however,  it  varies  with  the  particular  ones  used, 
and  he  was  able  to  draw  up  a  list  of  these,  similar  to  the  list  of 
substances  given  in  Par.  23,  so  arranged  that  any  one  becomes 
positively  electrified  when  touched  to  those  below  it  in  the  series 
but  negatively  electrified  when  touched  to  those  above  it.  Volta's 
list  comprised  seven  of  the  commoner  metals.  Such  a  list  now 
would  be  headed  by  the  alkaline  metals,  unknown  in  Volta's 
time,  and  would  be  ended  by  the  non-metal  carbon.  His  observa- 
tions were  merely  qualitative  but  subsequent  observers  have 
accurately  measured  these  differences  of  potential.  In  the  follow- 
ing list  the  numbers  between  the  names  indicate  the  difference  in 
potential  in  volts  set  up  between  the  corresponding  pairs  of  metals 
when  placed  in  contact: 

Zinc 

.210  volt 
Lead 

.069  volt 
Tin 

.313  volt 
Iron 

.146  volt 
Copper 

.238  volt 
Platinum 

.113  volt 
Carbon 

The  difference  of  potential  between  any  two  metals  in  the  series 
is  the  sum  of  the  intervening  numbers.  Thus,  with  a  zinc  and 
copper  pair,  the  difference  would  be  .738  volts  and  between  zinc 
and  carbon  it  is  1.089  volts. 

Regarding  as  negative  the  difference  of  potential  between  any 
pair  taken  in  reverse  order  from  that  given  in  the  above  list,  it 
follows  that  the  difference  in  potential  between  the  first  and  last 
metals  of  any  number  in  series  depends  only  upon  these  two  and 


148  ELEMENTS  OF  ELECTRICITY. 

is  independent  of  the  intervening  metals  or  of  the  order  in  which 
they  are  arranged.  Also,  no  matter  how  the  intervening  metals 
may  be  arranged,  there  is  no  difference  of  potential  between  the 
ends  of  a  series  beginning  and  ending  with  the  same  metal. 

The  foregoing  list  might  be  extended  to  include  other  substances 
than  the  metals.  For  example  (and  this  fact  is  extremely  impor- 
tant), a  difference  of  potential  is  produced  between  a  metal  and  a 
liquid  when  brought  into  contact  and  if  the  liquid  attacks  the 
metal  chemically,  an  electro-motive  force  will  act  from  the  metal 
towards  the  liquid.  Finally,  a  difference  of  potential  is  produced 
when  two  liquids  come  into  contact  and  even  between  solutions 
of  the  same  substance  when  these  solutions  are  of  different  degrees 
of  concentration. 

188.  Volta's  Contact  Theory. — While  there  is  no  uncertainty  as 
to  the  facts  as  set  forth  above,  there  has  been  much  controversy 
as  to  the  interpretation  to  be  put  upon  them.  According  to  Volta, 
when  two  dissimilar  metals  are  brought  together,  the  surface  of 
contact  becomes  a  seat  of  electro-motive  force  which  drives  posi- 
tive electricity  in  one  direction  from  the  junction  and  negative 
electricity  in  the  opposite,  and  this  separation  continues  until  the 
force  of  attraction  between  the  dissimilar  charges  balances  the 


A 

f~ 

-  COPPER    -«- 

-*•      ZINC   +1--^ 

i 
t 

V 

i 
i 

/ 

Fig.  92. 

force  which  drives  them  apart.  Thus  in  the  compound  bar  of 
copper  and  zinc,  Fig.  92,  the  zinc  end  becomes  positively  charged, 
the  copper  end  negatively,  or,  the  zinc  end  is  at  a  higher  potential 
than  the  copper. 

In  general,  when  bodies  at  different  potentials  are  connected  by 
a  conductor,  there  is  a  flow  of  electricity  from  the  one  of  higher 
potential  to  the  one  of  lower,  and,  unless  constantly  re-established, 
the  difference  of  potential  disappears.  It  would  therefore  seem 
that  in  this  case  if  B  be  connected  to  A  by  a  wire,  a  flow  of  elec- 
tricity would  take  place  from  B  to  A,  but  it  can  be  shown  that 
where  the  difference  of  potential  is  produced  by  contact  as  above 
and  the  metals  are  at  the  same  temperature,  it  is  not  possible  to 
get  such  a  flow.  If,  for  example,  the  connecting  wire  be  of  copper  or 


VOLTAIC  ELECTRICITY.  149X 

of  zinc,  the  effect  is  the  same  as  if  the  bar  in  Fig.  92  had  been  bent 
around  into  a  circle  until  the  ends  A  and  B  touched,  and  when 
these  ends  touch,  a  contact  electro-motive  force  is  set  up  equal 
but  opposite  to  the  one  already  existing  and  hence  just  counter- 
balancing it.  If  the  wire  be  of  some  third  metal,  it  follows  from 
Par.  187  that  to  whichever  end  of  the  bar  it  be  connected,  the 
electrical  effect  is  to  convert  the  bar  into  a  compound  one  con- 
sisting of  the  metal  of  the  remaining  end  and  of  that  of  the  wire,, 
and,  as  shown  above,  no  current  would  be  produced  upon  com- 
pleting the  circuit. 

Independent  theoretical  considerations  lead  to  the  same  con- 
clusion, for  if  a  current  flowed  through  the  wire  joining  B  and  A 
in  Fig.  92,  by  suitable  arrangements,  as  we  shall  see  later,  this 
current  could  be  made  to  do  mechanical,  chemical  or  thermal 
work  and  it  is  not  possible  that  the  mere  touching  of  two  metals 
should  be  a  source  of  such  energy. 

In  conclusion  we  may  say  that  even  considering  the  method 
described  in  Par.  186,  no  convincing  experimental  proof  of  Volta's 
theory  has  yet  been  devised. 

189.  Later  Theory. — Examination  of  the  series  as  given  in  Par. 
187  reveals  the  fact  that  the  metals  as  therein  arranged  are  in 
very  nearly  the  order  of  their  chemical  affinity  for  oxygen  as 
determined  by  the  heat  produced  by  the  combination  of  equiv- 
alent weights  of  these  metals  with  that  element.  The  difference 
of  potential  between  pairs  of  metals  therefore  measures  the 
difference  of  their  affinities  for  oxygen,  and  its  development  may 
be  explained  as  follows.  Consider  a  piece  of  zinc  in  air.  The 
molecules  of  oxygen  about  it  are  known  to  be  composed  each  of 
two  atoms,  and,  as  we  shall  see  later,  there  is  reason  to  believe 
that  these  atoms  carry  equal  and  opposite  charges  of  electricity 
and  are  held  together  in  the  molecules  by  the  mutual  attraction 
of  these  elementary  charges.  Under  the  influence  of  atmospheric 
moisture  (Par.  281)  the  zinc  slowly  tarnishes  or  oxidizes.  The 
oxygen,  in  order  to  combine  with  the  zinc,  must  first  separate 
into  atoms  and  it  is  the  negatively-charged  atoms  that  enter  into 
the  combination,  each  giving  up  to  the  zinc  its  charge  as  it  does  so. 
The  zinc,  therefore,  becomes  negatively  charged  and  is  surrounded 
by  a  layer  of  positively-charged  oxygen  atoms.  A  piece  of  copper 
would  behave  similarly  but  having  a  less  affinity  for  oxygen  it 
would  acquire  a  smaller  negative  charge  and  the  oxygen  about  it 


150  ELEMENTS  OF  ELECTRICITY. 

would  be  less  highly  charged  positively.  This  state  of  affairs  is 
represented  graphically  in  Fig.  93.  No  indication  of  these  charges 
could  be  detected  by  an  electrometer,  for  the  charges  upon  the 
pieces  of  metal  and  in  the  surrounding  air  being  equal  and  opposite 
produce  no  external  effect.  If,  however,  the  two  metals  be  touched 
together,  they,  being  conductors,  come  at  once  to  a  common 
potential,  but  the  air  being  a  non-conductor,  that  about  the  zinc 


©00© 

©      to 
©     © 

Fig.  93. 

©      ©      © 

I        ZINC 

-    COPPER    - 

©©  ©© 

©       ©      © 

is  left  at  a  higher  potential  than  that  about  the  copper.  We  there- 
fore have  good  reason  to  believe  that  the  difference  of  potential 
between  pairs  of  metals  as  measured  by  electrometers  is  really  the 
difference  of  potential  between  the  layers  of  air  surrounding  the 
metals  and  not  that  between  the  metals  themselves.  This  view 
is  corroborated  by  the  observed  changes  in  the  difference  of  poten- 
tial when  pairs  of  metals  are  surrounded  by  other  gases  than  air 

190.  The  Voltaic  Pile. — By  means  of  his  condensing  electro- 
scope Volta  demonstrated,  as  he  thought,  the  difference  of  poten- 
tial produced  at  the  ends  of  a  zinc-copper  bar  but  was  unable  to 
detect  any  current  in  the  wires  by  which  he  joined  the  ends  of  the 
bar.  In  Par.  188  above,  it  has  been  shown  that  there  is  no  such 
current,  but  Volta,  thinking  that  there  was  one  but  so  feeble  as  to 
elude  his  instruments,  sought  some  way  of  multiplying  its  effect 
and  endeavored  to  combine  the  supposed  currents  from  a  number 
of  zinc-copper  pairs.  He  began  by  arranging  in  a  pile  a  series  of 
discs,  alternately  copper  and  zinc,  but  at  once  encountered  a  diffi- 
culty. According  to  his  theory,  from  the  junction  of  the  bottom 
copper  disc  with  the  zinc  disc  above  it  a  positive  current  ascended, 
a  negative  current  descended,  but  when  the  second  copper  disc 
was  reached  this  was  reversed,  a  positive  current  descended  and  a 
negative  current  ascended,  and  so  on.  In  other  words,  the  upward 
currents  were  alternately  positive  and  negative  and  alternated  in 
this  respect  with  the  downward  currents.  With  an  even  number 
of  discs  the  net  result  was  no  greater  than  with  two;  with  an  odd 
number  the  net  result  was  zero.  Since  these  currents  were  sup- 


VOLTAIC  ELECTRICITY.  151 

posed  to  originate  at  the  surface  of  contact  of  the  two  metals,  if 
the  copper  plates  were  separated  from  the  zinc  plate  immediately 
below  them,  the  contrary  currents  would  be  eliminated.  He  there- 
fore inserted  between  these  plates  a  disc  of  cloth,  

Fig.  94,  but  since  cloth  is  a  non-conductor  he     I    c*™^     1 
moistened  it  with  water.     Water  is  a  poor  con-     __^ 

ductor  (Par.  276)  but  its  ability  to  conduct  is     | 'ZINC 

greatly  improved  by  dissolving  in  it  a  small 

amount  of  salt  or  of  acid.   His  invention  therefore 

took  the  final  form,  as  shown  in  Fig.  94,  of  a 

pile  of  pairs  of  zinc  and  copper  discs  separated 

by  layers  of  cloth  or  of  blotting  paper  which  had 

been  soaked  in  brine  or  in  dilute  acid.    The  results 

far  exceeded  his  expectations.    The  difference  of 

potential  between  the  top  and  bottom  of  the  pile  varied  directly 

with  the  number  of  pairs  of  discs  used.    If  the  top  and  bottom 

discs  were  touched  simultaneously,  there  was  experienced  a  shock, 

milder  than  that  of  the  Leyden  jar  but  continuous.    By  means  of 

wires  attached  to  the  extremities  of  the  pile,  electrical  apparatus 

could  be  charged.    If  these  wires  were  touched  together  and  then 

separated,  a  spark  was  produced,  etc. 

The  voltaic  pile  was  made  known  to  the  scientific  world  in  March 
of  1800  and  has  long  since  been  relegated  to  the  museum  shelf,  but 
its  invention,  nevertheless,  marks  an  epoch  in  the  history  of  elec- 
tricity. It  gave  a  fresh  impetus  to  the  science,  which  in  the  next 
few  years  advanced  by  bounds,  and  it  put  into  the  hands  of  the 
chemist  a  new  agent  which  for  the  first  time  enabled  him  to  decom- 
pose water  into  its  constituent  elements  and  made  known  to  him 
the  metals  of  the  potassium  and  calcium  groups. 

191.  Volta's  Circlet  of  Cups. — Volta  soon  noticed  that  the  power 
of  his  pile  fell  off  after  a  short  use  and  he  attributed  this  to  the  loss 
of  the  conducting  liquid  in  the  layers  of  cloth,  partly  by  being 
squeezed  out  by  the  weight  of  the  metal  discs  and  partly  by  evapo- 
ration. To  remedy  this  he  devised  a  plan  which  will  be  under- 
stood from  the  following  explanation.  Let  us  suppose  the  pile  to 
be  laid  on  its  side,  as  represented  in  Fig.  95  a.  Since  he  had 
shown  that  the  electrification  by  contact  was  independent  of  the 
extent  of  the  surfaces  in  contact,  the  same  effect  would  be  pro- 
duced if  the  copper  and  zinc  pairs  were  separated  and  touched 
only  at  the  top  as  shown  in  6.  Being  spread  apart  in  this  way, 


152 


ELEMENTS  OF  ELECTRICITY. 


glass  cups,  represented  by  the  dotted  lines,  could  be  slipped  under 
the  pairs  which  were  separated  by  the  moistened  cloth,  the  cloth 
could  then  be  withdrawn,  and  the  cups  filled  with  the  liquid  itself. 
This  modified  form  very  quickly  displaced  the  original  pile.  The 
individual  cups  are  designated  cells,  and  a  series  of  two  or  more 
is  called  a  battery,  the  primary  meaning  of  the  word  battery  being 


1 

1 

1 

1 

i  i 

\ 

j 

a 


Fig.  95. 


a  number  of  similar  utensils  placed  side  by  side.  For  use  with 
these  batteries,  the  zinc-copper  pairs  were  in  the  form  of  a  strip 
joined  at  the  middle  and  bent  into  the  arc  of  a  circle  so  as  to  be 
inserted  into  the  cups.  This  is  the  origin  of  such  terms  as  "con- 
nected in  multiple  arc"  applied  to  certain  groupings  of  cells  to  be 
described  later.  An  arrangement  of  cells  in  a  circle  by  which  the 


Fig.  96. 

positive  and  negative  ends  of  the  battery  could,  for  convenience, 
be  brought  close  together  (Fig.  96),  was  called  by  Volta  his  "cour- 
onne  de  lasses"  or  circlet  of  cups. 

192.  Source  of  Electrical  Energy  in  a  Cell. — It  will  have  been 
noted  that  in  Par.  188  the  statement  was  made  that  no  current 
could  be  produced  by  the  contact  of  dissimilar  metals,  yet  Volta, 
proceeding  on  the  contrary  assumption  devised  the  pile  and  the 
battery,  both  of  which  produce  a  continuous  supply  of  electricity. 


VOLTAIC  ELECTRICITY.  153 

In  Par.  189  we  saw  that  when  zinc  and  copper  are  brought  to- 
gether in  air,  the  metals,  being  good  conductors,  come  to  a  common 
potential  and  the  air  surrounding  the  zinc  is  left  at  a  higher 
potential  than  that  around  the  copper.  When,  however,  these 
metals  are  immersed  in  a  chemically  active  liquid,  a  different  state 
of  affairs  results,  for  in  this  case  the  medium  surrounding  the 
metals,  instead  of  being  a  non-conductor  like  the  air,  is  a  con- 
ductor and  hence  at  a  uniform  potential.  We  also  saw  (Par.  187) 
that  when  a  metal  is  attacked  by  a  liquid,  an  electro-motive  force 
is  set  up  from  the  metal  towards  the  liquid.  In  this  case,  the  zinc 
being  the  more  vigorously  attacked,  the  electro-motive  force 
acting  from  the  zinc  is  greater  than  that  acting  from  the  copper; 
positive  electricity  is  therefore  driven  across  from  the  zinc  to  the 
copper  and  the  zinc  itself  is  left  negatively  charged.  The  copper 
is,  therefore,  at  a  higher  potential  than  the  zinc  and  if  it  be  con- 
nected to  the  zinc  by  a  wire,  a  current  will  flow  through  this  wire 
from  the  copper  to  the  zinc.  The  source  of  the  electrical  energy 
in  these  arrangements  is  not  at  the  junction  of  the  two  metals  but 
at  the  point  of  contact  of  the  zinc  with  the  brine  or  the  dilute 
acid  and  is  due  to  the  chemical  action  which  there  takes  place. 
For  this  reason,  the  left  hand  copper  strip  and  the  right  hand  zinc 
strip  in  Fig.  95  b  can  be  omitted,  as  shown  in  Fig.  96,  without 
affecting  the  strength  of  the  battery.  See  also  Par.  279. 


154 


ELEMENTS  OF  ELECTRICITY. 


CHAPTER  19. 
THE   SIMPLE   CELL. 

193.  Simple  Voltaic  Cell. — A  voltaic  cell  in  its  simplest  form 
consists  (Fig.  97)  of  a  glass  cup  partly  filled  with  acidulated  water, 
called  the  electrolyte,  into  which  dip  a  strip  of  copper  and  one  of 
zinc,  sometimes  spoken  of  as  the  elements  of  the  cell.  We  shall 

suppose  that,  as  represented  in 
Fig.  97,  to  each  of  these  strips 
there  is  attached  a  wire.  If  the 
zinc  be  pure,  or  if  it  has  been 
COPPER  treated  as  will  be  explained  later 
(Par.  197),  no  action  will  be 
observed  so  long  as  the  strips 
are  kept  apart.  If,  however, 
they  are  inclined  towards  each 
other  so  as  to  touch  either  above 
or  below  the  surface  of  the  liquid, 
or  if  they  be  brought  into  con- 
tact indirectly  by  joining  the  ends 
of  the  two  wires,  then  bubbles 
of  gas  will  immediately  appear 
on  the  surface  of  the  copper  and 

the  zinc  will  be  observed  to  dissolve  away  gradually.  This  cor- 
rosion of  the  zinc  and  evolution  of  bubbles  will  continue  only  so 
long  as  the  strips  are  in  contact  or  the  wires  are  connected, 
and  during  this  time  a  current  of  electricity  will  flow  through 
the  liquid  from  the  zinc  to  the  copper  and  from  the  copper 
through  the  point  of  contact  of  the  two  strips,  or  through  the 
connecting  wire,  back  to  the  zinc.  Since,  as  we  shall  shortly 
see  (Par.  217),  we  can  not  be  positive  in  which  direction  the 
current  does  flow,  we,  by  convention  and  from  analogy  with 
water,  agree  to  consider  that  it  flows  from  the  point  of  high 
potential  to  that  of  lower,  or  from  positive  to  negative;  there- 
fore, since  the  current  is  due  to  the  chemical  energy  developed 
on  the  surface  of  the  zinc  and  originates  there,  the  zinc  plate  is 


Fig.  97. 


VOLTAIC  ELECTRICITY.  155 

called  the  positive  plate  and  consequently  the  copper  is  the  nega- 
tive plate.  The  current  crosses  the  liquid  to  the  copper  plate, 
ascends  this  plate  to  the  attached  wire,  follows  along  the  wires  to 
the  junction  with  the  zinc  plate  and  descends  this  plate  to  the 
point  of  starting.  The  points  of  attachment  of  the  wires  to  the 
copper  and  zinc  are  called  the  poles  of  the  cell,  and  since  the  current 
flows  from  the  copper  out  into  the  connecting  wire,  the  copper 
pole  is  called  the  positive  pole,  the  zinc,  the  negative  pole.  On 
account  of  the  confusion  sometimes  resulting  from  this  nomencla- 
ture, it  is  perhaps  unfortunate  that  the  copper  should  be  both  the 
positive  pole  and  the  negative  plate  and  that  the  zinc  should  be 
the  positive  plate  but  the  negative  pole.  As  an  aid  to  the  beginner 
it  may  be  remembered  that  the  positive  plate  is  the  one  which  is 
attacked  by  the  electrolyte  and  is  the  point  of  origin  of  the  current. 

194.  Material  Used  for  Elements  of  a  Cell.—  The  elements  of  a 
cell  are  usually  metal,  or  carbon  and  a  metal.    The  farther  apart 
the  elements  are  on  the  list  as  given  in  Par.  187,  the  more  vigorous 
will  be  the  chemical  action  set  up  in  the  cell  and  consequently  the 
greater  the  electrical  energy  developed.    The  positive  plate  should 
be  of  the  metal  most  freely  attacked  by  the  electrolyte;  the  nega- 
tive plate  should  be  of  the  metal  attacked  least.    The  alkaline 
and  the  alkaline-earth  metals  head  the  list  but  decompose  water 
and  combine  with  acids  with  almost  explosive  violence;  they  are, 
therefore,  unfitted  for  use.    The  most  suitable  metal  for  the  posi- 
tive plate,  both  from  the  standpoint  of  chemical  action  and  of 
cost,  is  zinc,  while  carbon,  copper  and  platinum  are  the  substances 
most  frequently  used  as  negative  plates. 

195.  Chemical  Action  in  a  Simple  Cell.—  If  the  electrolyte  of 
the  simple  cell  be  dilute  sulphuric  acid,  the  chemical  action  when 
the  circuit  is  closed  is  in  accordance  with  the  following  reaction: 


The  zinc  sulphate  passes  into  solution  as  it  is  formed  and  the 
hydrogen  is  evolved  as  bubbles  at  the  surface  of  the  copper  plate. 
Since  the  chemical  action  takes  place  at  the  surface  of  the  zinc, 
it  would  seem  that  the  hydrogen  bubbles  should  be  released  at  that 
point  or  else  that  they  should  be  seen  passing  through  the  liquid 
to  reach  the  copper  plate.  The  reason  why  neither  of  these  occur 
is  explained  in  Par.  274. 


156  ELEMENTS  OF  ELECTRICITY. 

If  the  hydrogen  be  collected  under  an  inverted  jar  and  its  weight 
be  determined,  and  if  the  zinc  plate  be  weighed  at  the  beginning 
and  conclusion  of  the  experiment,  it  is  found  that  while  two  parts 
of  hydrogen  are  being  produced,  65  parts  of  zinc  are  eaten  away, 
that  is,  chemically  equivalent  amounts  of  the  two  are  evolved 
and  dissolved  respectively,  or  the  action  is  strictly  chemical. 

Instead  of  dilute  acid  a  saline  solution  is  often  used  as  an  electro- 
lyte, ammonium  chloride  being  frequently  employed.  The  reac- 
tion in  this  case  is 

Zn+2NH4Cl  =  ZnCl2+2NH3+H2 

both  the  zinc  chlo- 
ride and  the  ammonia  passing  into  solution. 

196.  Local  Action. — In  Par.  193  it  was  stated  that  if  a  plate  of 
pure  zinc  be  dipped  into  dilute  sulphuric  acid,  no  effect  would  be 
produced.    Commercial  zinc,  however,  is  far  from  being  pure  and 
contains  appreciable  amounts  of  iron,  lead  and  other  substances. 
If  such  a  plate  be  dipped  into  the  electrolyte,  chemical  action 
immediately  ensues,  bubbles  of  hydrogen  gas  are  evolved,  the  plate 
becomes  pitted  and  may  eventually  be  eaten  through,  and  the 
acid  becomes  spent.    The  explanation  is  that  the  minute  particles 
of  the  foreign  metal  in  contact  with  the  zinc  constitute  tiny  voltaic 
pairs,  local  currents  set  up  from  the  zinc  through  the  electrolyte 
to  the  particles  and  back  to  the  zinc,  and  cup-shaped  depressions 
are  eaten  out  around  these  particles  until  the  latter  become  dis- 
engaged and  fall.    This  process  is  called  local  action.    The  currents 
produced  are  parasitic  and  wasteful,  existing  at  the  expense  of  the 
materials  of  the  cell  but  contributing  nothing  to  its  useful  energy. 

The  rapid  rusting  of  a  nickel-plated  piece  of  iron,  once  that  the 
nickel  coating  is  cut  through,  and  the  corrosion  about  the  heads  of 
iron  nails  driven  through  the  copper  sheathing  of  vessels  is  similar 
to  this  local  action. 

197.  Remedy  for  Local  Action. — The  logical  remedy  for  local 
action  would  be  the  use  of  chemically  pure  zinc  but  the  cost 
renders  this  prohibitive.    However,  in  1830  it  was  discovered  that 
local  action  can  be  almost  entirely  obviated  if  the  surface  of  the 
zinc  be  amalgamated,  that  is,  covered  with  a  thin  layer  of  mercury. 
This  may  be  done  either  by  adding  about  four  per  cent  of  mercury 
to  the  zinc  at  the  time  when  it  is  cast  into  plates,  or  by  cleaning 
the  surface  by  dilute  acid  and  then  rubbing  mercury  upon  it  with 
a  bit  of  rag.    The  mercury  unites  with  the  zinc  forming  a  sort  of 


VOLTAIC  ELECTRICITY.  157 

silvery  paste  but  does  not  dissolve  the  particles  of  iron  which  are 
either  covered  up  or  else  float  to  the  surface  of  the  amalgam  and 
drop  off.  As  the  zinc  in  the  amalgam  is  eaten  away  during  use  of 
the  cell,  the  mercury  amalgamates  new  layers  of  the  zinc  beneath. 
The  action  of  the  amalgam  is  not  thoroughly  understood,  for, 
apparently,  by  adding  the  mercury  we  have  brought  about  the 
exact  condition  which  we  wished  to  avoid,  that  is,  contact  of  two 
dissimilar  metals  in  presence  of  the  acid. 

198.  Polarization. — If  the  wires  attached  to  the  poles  of  a  simple 
cell  be  brought  into  contact,  a  current  will  immediately  flow 
through  the  circuit,  but  if  it  be  measured  by  any  of  the  means  to 
be  described  later,  this  current  will  be  found  to  fall  off  rapidly. 
If  the  copper  plate  be  observed,  it  will  be  noted  that  not  all  of  the 
hydrogen  bubbles  released  at  this  plate  rise  to  the  top  but  many 
remain  adhering  to  it  and  the  surface  of  the  plate  rapidly  acquires 
a  silvery  bloom.  The  negative  plate  is  then  said  to  be  polarized. 
It  is  this  layer  of  hydrogen  which  causes  the  current  to  dwindle 
and  it  does  so  in  two  ways,  one  mechanical,  the  other  electro- 
chemical. First,  the  hydrogen  being  a  non-conductor,  each  bubble 
in  contact  with  the  copper  withdraws  just  so  much  of  the  surface 
of  this  plate  from  contact  with  the  liquid  and  diminishes  by  just 
so  much  the  cross-section  of  the  path  available  for  the  passage  of 
the  current.  It  therefore  cuts  down  the  current  by  putting  resist- 
ance in  its  path.  Second,  the  film  of  bubbles  upon  the  plate  causes 
it  to  approximate  in  behavior  to  a  plate  of  hydrogen,  and  since 
hydrogen  has  a  greater  tendency  to  oxidize  than  has  copper,  the 
effect  is  to  set  up  a  greater  electro-motive  force  opposed  in  direc- 
tion to  that  from  the  zinc.  We  have  seen  (Par.  192)  that  it  was  the' 
difference  between  the  electro-motive  forces  acting  from  the  zinc 
and  from  the  copper  which  drove  the  current  through  the  cell, 
consequently,  when  this  difference  becomes  smaller,  the  current 
also  becomes  smaller. 

This  diminution  of  the  current  by  polarization  may  be  avoided 
by  surrounding  the  negative  plate  by  some  agent,  either  solid  or 
liquid,  which  will  oxidize  the  hydrogen,  converting  it  into  water, 
or  will  enter  into  combination  with  it,  releasing  in  its  stead  some 
element  which  does  not  increase  the  resistance  of  the  negative 
plate.  The  endeavor  to  do  away  with  this  polarization  is  largely 
responsible  for  the  different  varieties  of  cells  described  in  the  fol- 
lowing chapter. 


158  ELEMENTS  OF  ELECTRICITY. 

199.  Depolarizers. — Among  the  many  substances  which  have 
been  employed  for  this  oxidation  of  the  hydrogen  are  the  liquids 
nitric  acid,  solutions  of  nitrate  of  potassium,  of  the  bichromates 
of  potassium  and  sodium,  of  ferric  chloride,  etc.,  and  the  solids 
black  oxide  of  manganese,  peroxide  of  lead,  and  oxide  of  copper. 
The  solid  depolarizers  may  be  made  into  a  pasty  mass  and  moulded 
about  the  negative  plate  or  may  be  made  into  briquettes  and 
fastened  to  the  negative  plate  by  rubber  bands.    The  liquid  de- 
polarizers may  sometimes  be  mixed  with  the  electrolyte  but  in 
most  cases  would  attack  the  positive  plate,  even  when  the  circuit 
was  open,  therefore,  to  prevent  their  reaching  the  positive  plate 
but  at  the  same  time  not  to  hinder  the  passage  of  the  current, 
they  are  usually  put  along  with  the  negative  plate  in  an  interior 
unglazed  and  porous  porcelain  cup  which  is  placed  in  the  electro- 
lyte.    Such  cells  are  sometimes  called  two-fluid  cells. 

200.  Requirements  of  a  Voltaic  Cell. — The  properties  desired  in 
a  good  primary  cell  are  the  following: 

(1)  It  should  have  a  high  and  constant  electro-motive  force, 

preferably  greater  than  one  volt. 

(2)  It  should  have  low  internal  resistance. 

(3)  It  should  give  a  constant  current  and  should,  therefore,  be 

free  from  polarization. 

(4)  It  should  be  free  from  local  action,  its  elements  not  being 

consumed  except  when  it  is  supplying  current. 

(5)  Its  elements  should  be  cheap.    The  cost  of  plates  of  gold, 

platinum  or  silver  is  in  most  cases  prohibitive. 

(6)  Its  elements  should  be  durable,  not  requiring  too  frequent 

renewal  or  too  much  attention. 

(7)  It  should  not  emit  corrosive  or  poisonous  fumes. 

(8)  The  electrolyte  should  not  freeze  readily. 

No  cell  has  yet  been  devised  which  fulfills  all  of  these  conditions, 
and  for  different  uses  they  are  not  equally  important.  For  example, 
constancy  of  current,  while  essential  when  a  small  electrical  ma- 
chine, such  as  a  fan,  is  to  be  run,  is  not  so  where  the  cells  are  used 
intermittently  and  then  only  for  very  brief  periods,  as  is  the  case 
with  those  that  operate  door  and  call  bells.  Again,  for  telegraphy 
over  a  long  line  of  considerable  resistance,  a  moderate  internal 
resistance  of  the  cell  is  not  very  objectionable. 

The  E.  M.  F.  of  a  cell  is  independent  of  the  size  of  its  plates  or 


VOLTAIC  ELECTRICITY.  159 

of  the  depth  to  which  they  are  immersed  in  the  electrolyte,  that  is, 
of  the  size  of  the  cell,  but  depends  entirely  upon  the  relative  posi- 
tion of  its  elements  in  Volta's  series  (Par.  187).  The  E.  M.  F.  of 
a  zinc-copper-sulphuric  acid  cell  is  the  same  whether  the  cell  be  as 
large  as  a  barrel  or  as  small  as  a  thimble.  Therefore,  the  elements 
of  a  cell  having  been  selected,  its  E.  M.  F.  is  fixed.  The  quantity 
of  electricity  produced  varies,  however,  with  the  amount  of  chemi- 
cal action  in  the  cell  and  this  varies  directly  with  the  size  of  the 
plates. 


160  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  20. 

KINDS   OF   CELLS. 

201.  Great  Variety  of  Cells. — Any  two  conducting  substances 
which  dip  into  a  vessel  containing  a  liquid  which  attacks  one  more 
than  it  does  the  other,  constitute  a  primary  cell,  also  called  a  voltaic 
or  a  galvanic  cell.    There  are,  therefore,  a  great  many  possible 
arrangements  by  which  electricity  may  be  generated  by  chemical 
means  and  this  number  is  still  further  increased  when  we  consider 
the  many  expedients  adopted  for  avoiding  polarization.    It  would 
therefore  seem  that  the  number  of  kinds  of  cells  would  be  limited 
only  by  the  ingenuity  of  the  inventor  and  such  would  be  the  case 
were  it  not  for  the  required  conditions  (Par.  200)  which  not  being 
fulfilled  by  the  majority  of  the  possible  combinations  cause  these 
combinations  to  be  rejected.    Notwithstanding  this,  the  variety 
is  still  great  and  the  few  described  in  the  following  pages  must 
be  regarded  as  types  of  general  classes. 

202.  Classification  of  Cells. — Cells  may  be  divided  into  two 
general  classes,  primary  and  secondary.     The  primary  cell  has 
been  defined  above  (Par.  201) ;  the  secondary  cell  differs  from  the 
primary  mainly  in  that  when  it  has  become  exhausted,  an  electric 
current  may  be  passed  through  it  in  a  contrary  direction  to  the 
current  which  it  supplied,  the  chemical  changes  which  have  taken 
place  may  be  undone  and  the  cell  can  be  restored  to  its  primitive 
condition.    It  is  therefore  analogous  to  a  clock  which,  when  run 
down,  can  be  wound  up  again.    Secondary  cells  are  used  in  storage 
batteries  and  will  be  considered  in  detail  when  we  reach  that  subject 
(Chapter  22). 

Primary  cells  are  of  two  classes,  those  without  depolarizers 
(such  as  the  simple  cell  described  in  Par.  193),  and  those  with 
depolarizers.  This  latter  class  may  be  subdivided  according  as 
the  depolarizer  is  a  liquid  or  a  solid.  Other  subdivisions  may  be 
made,  as,  for  example,  single-fluid  cells,  two-fluid  cells,  dry  cells, 
standard  cells,  etc.,  but  this  classification  is  not  of  sufficient  im- 
portance to  be  dwelt  upon  longer. 


VOLTAIC  ELECTRICITY. 


161 


203.  Grove's  Cell. — One  of  the  first  cells  in  which  a  chemical 
depolarizer  was  employed  was  invented  by  Grove  in  1839.    This 
consists  (Fig.  98)  of  a  flattened,  rectangular  outer  cell  A  of  glass 
or  of  vulcanized  rubber,  containing  dilute 
sulphuric  acid  into  which  dips  the  U-shaped 
amalgamated  zinc  plate   B.     Within  the 
loop  of  this  zinc  plate  there  fits  a  flat  porous 
cell  C  containing  concentrated  nitric  acid 
and  the  platinum  negative  plate  D.    The 
hydrogen  produced  by  the  action  in  the 
external  cell  is  attacked  by  the  nitric  acid 
as  follows: 

3H+HN03=2H20+NO 


Fig.  98. 


The  nitric  oxide,  NO,  produces  no  polar- 
ization since  it  either  dissolves  in  the  acid 
or  escapes  into  the  air  where,  in  contact  with 
oxygen,  it  becomes  nitric  peroxide,  N02,  a 
reddish  brown,  irritating  gas.  The  cell  has  a  high  electro-motive 
force,  very  nearly  two  volts,  and  owing  to  the  great  amount  of 
surface  of  the  zinc  plate  and  the  short  dis- 
tance from  the  zinc  to  the  platinum  plate, 
it  has  small  internal  resistance.  The  objec- 
tions to  this  cell  are  the  corrosive  and 
poisonous  character  of  the  nitric  peroxide 
fumes  and  the  cost  of  the  platinum  plates. 
These  last  need  be  no  thicker  than  tin-foil 
but  since  the  cost  of  platinum  is  now  (1912) 
more  than  that  of  gold  (about  $700  per 
pound  avoirdupois),  they  are  necessarily 
very  expensive. 

204.  The  Bunsen  Cell.  —  To  avoid  the 
expense  of  the  platinum  plate,  Bunsen,  in 
the  year  following  the  invention  of  the 
Grove  cell,  suggested  the  use  in  its  stead 
of  a  plate  of  hard  carbon.  These  plates 
are  prepared  from  gas  coke  or  that  par- 
ticular hard  and  semi-metallic  form  of  carbon  resulting  from  the 
decomposition  by  heat  of  gaseous  hydro-carbons  and  occurring 
as  a  deposit  in  the  retorts  and  flues  of  gas  works.  The  principle 


Fig.  99. 


162 


ELEMENTS  OF  ELECTRICITY. 


of  the  Bunsen  cell  is  precisely  the  same  as  that  of  Grove's  cell. 
The  carbon  plate  (C,  Fig.  99)  is  in  shape  a  square  prism  and  dips 
into  nitric  acid  in  an  inner  porous  cup.  The  zinc  plate  Z  is  a 
split  cylinder  and  embraces  this  inner  cup.  The  cell  gives  off  the 
same  corrosive  fumes  as  the  Grove  cell  but  the  greatest  objection 
to  it  is  the  difficulty  of  making  electrical  connection  with  the 
carbon  plate.  This  plate  being  porous,  it  is  difficult  to  attach 
wires  to  it  directly.  To  remedy  this,  the  upper  end  of  the  plate 
is  sometimes  copper  plated,  after  which  the  connector  is  clamped 
to  it  as  shown  in  Fig.  99.  Also,  owing  to  its  porosity,  the  plate 
soaks  up  the  nitric  acid  which,  upon  rising  to  the  height  of  the 
copper  plating  or  of  the  connecting  wires,  will  corrode  the  con- 
nections. This  is  partly  remedied  by  soaking  the  upper  end  of 
the  plate  in  melted  paraffine  which,  being  impervious  to  the  acid, 
hinders  its  rise. 

205.  The  Bichromate  Cell. — There  are  a  number  of  cells  which 
instead  of  nitric  acid  employ  either  chromic  acid  or  the  bichro- 
mates of  potassium  or  of  sodium  as  depolarizers,  but  are  otherwise 
the  same  as  the  Bunsen  cell.  It  is  found 
that  in  these  the  inner  porous  cell  is  not 
necessary  and  the  bichromate  solution 
may  be  allowed  to  mingle  freely  with  the 
sulphuric  acid,  in  fact,  they  are  sold  ready 
mixed  under  the  name  electropoion  fluid. 
The  hydrogen  released  by  the  action  of 
the  sulphuric  acid  upon  the  zinc  is  oxi- 
dized by  the  bichromate,  the  products 
being  water  and  chrome  alum  thus 


K2Cr207+4H2S04  +  6H  = 
2KCr(S04)2+7H20 

206.  Daniell's  Cell.  — The  first  cell  to 
avoid  polarization  was  invented  by  Daniell 
in  1836  and,  although  using  a  liquid  de- 
polarizer, the  principle  of  its  action  is  quite 

different  from  that  of  the  cells  described 
FIE    100 

in   the  preceding  paragraphs.    Fig.    100 

represents  one  of  its  many  forms.  This  consists  of  an  inner 
porous  cup,  which  contains  dilute  sulphuric  acid,  and  the  zinc 
plate.  The  zinc  is  given  the  corrugated  form  shown  in  the  figure 


VOLTAIC  ELECTRICITY.  163 

in  order  to  expose  more  surface  to  the  action  of  the  acid.  The 
copper  plate,  in  the  form  of  a  split  cylinder,  surrounds  the  inner 
cup  and  is  immersed  in  a  solution  of  copper  sulphate  contained 
in  the  outer  cell.  As  it  is  important  that  this  last  solution  should 
be  kept  saturated,  there  is  fastened  to  the  side  of  the  copper  plate 
a  little  cup  or  shelf  with  perforated  bottom  and  this  cup  is  kept 
filled  with  crystals  of  copper  sulphate. 

The  chemical  action  in  the  inner  cell  is  the  same  as  already 
described  but  the  hydrogen  on  coming  in  contact  with  the  copper 
sulphate  solution  displaces  the  copper  and  takes  its  place  and 
the  copper  is  deposited  on  the  negative  plate  thus 


There  is,  therefore,  no  polarization  and  the  copper  plate  simply 
grows  thicker  by  the  deposition  upon  its  surface  of  successive  films 
of  copper.  The  copper  sulphate  solution  would,  however,  become 
gradually  exhausted  were  it  not  continually  replenished  from  the 
crystals  on  the  perforated  shelf. 

The  sulphuric  acid  in  the  inner  cup  is  gradually  converted  to  a 
solution  of  zinc  sulphate  but  the  cell  continues  to  operate,  in  fact, 
the  inner  cup  is  often  filled  from  the  beginning  with  a  solution  of 
zinc  sulphate.  In  this  case  the  following  reaction  takes  place: 


the  copper  being  deposited  upon  the  negative  plate  as  before  and 
the  sulphion,  S04,  attacking  fresh  portions  of  the  zinc  and  again 
becoming  zinc  sulphate. 

The  electro-motive  force  of  a  Daniell  cell  averages  about  1.07 
volts  but  fluctuates  slightly  with  the  variation  in  the  strength 
of  the  two  solutions  and  also  with  the  temperature.  Being  free 
from  polarization,  it  is  very  largely  used  where  constant  currents 
are  required,  as  is  especially  the  case  in  telegraphy  in  this  country. 

207.  Gravity  Cell.  —  A  saturated  solution  of  copper  sulphate 
has  a  specific  gravity  of  about  1.20  and  if  the  specific  gravity^  of 
the  zinc  sulphate  solution  be  kept  below  this  figure,  it  is  possible 
to  do  away  with  the  inner  cup  of  the  Daniell  cell  and  to  separate 
the  two  fluids  by  the  difference  in  their  densities.  Such  a  cell, 
called  a  gravity  cell,  is  represented  in  Fig.  101.  The  copper  plate, 
of  the  shape  shown,  is  placed  upon  the  bottom  of  the  cell  and 
the  copper  sulphate  solution  with  extra  crystals  is  poured  over  it. 
The  wire  from  this  plate  is  protected  by  rubber  or  by  a  glass 


164 


ELEMENTS  OF  ELECTRICITY. 


tube  up  to  the  top  of  the  cell.    The  zinc  plate,  of  the  shape  shown, 
is  hung  from  the  edge  of  the  cell  and  is  covered  with  a  dilute 

solution  of  zinc  sulphate.  As  the  cell  is 
used  the  zinc  sulphate  solution  increases 
in  density.  It  must  therefore  be  tested 
from  time  to  time  by  means  of  a  hydrom- 
eter (a  little  graduated  glass  float  which 
stands  higher  in  the  liquid  as  the  latter 
grows  denser,  and  sinks  lower  as  it  grows 
less  dense),  and  should  the  density  reach 
1.15,  a  portion  of  the  solution  must  be 
drawn  off  by  a  syringe  or  a  siphon  and 
water  added  in  its  place.  If  the  cell  be 
unused  for  some  time,  the  two  fluids  will 
mingle  by  diffusion  and  when  the  copper 
sulphate  solution  reaches  the  zinc  plate, 
metallic  copper  will  be  deposited  upon 
this  plate  with  the  result  that  local  action 
will  ensue. 


Fig.  101. 


From  the  shape  of  the  zinc  plate,  these  cells  are  commonly 
loiown  as  crowfoot  batteries. 

208.  The  Edison-Lalande  Cell. — This  is  an  example  of  a  cell 
employing  a  solid  depolarizer.  It  has  two 
positive  plates  of  zinc  bolted  together  at  the 
top  and  arranged  one  on  either  side  of  the 
negative  plate.  This  last  is  of  cupric  oxide 
compressed  into  the  required  shape  and  size. 
During  the  process  there  is  added  some 
cementing  material  which  when  heated  binds 
the  particles  firmly  together.  The  com- 
pleted plate  is  inserted  in  a  copper  frame  by 
which  it  is  suspended  from  the  lid  of  the  cell. 
The  arrangement  is  shown  in  Fig.  102  in 
which,  for  the  sake  of  clearness,  one  of  the 
zinc  plates  has  been  omitted .  The  electrolyte 
is  a  solution  of  caustic  potash  (potassium 
hydroxide)  which  when  the  circuit  is  closed  attacks  the  zinc,  pro- 
ducing a  double  oxide  of  zinc  and  potassium  (potassium  zincate) 
and  releasing  hydrogen,  thus 

Zn  +2KOH  =  K2Zn02+H2 


Fig.  102. 


VOLTAIC  ELECTRICITY. 


165 


The  hydrogen  reduces  the  copper  oxide  of  the  negative  plate  as 
follows: 

H2-f-CuO  =  H20+Cu 

and  there  is  therefore 
no  polarization. 

The  electro-motive  force  of  these  cells  is  low  (only  .7  volt),  but 
the  internal  resistance  is  very  small  and  their  efficiency  is  high. 

Potassium  hydroxide  has  a  great  affinity  for  carbon  dioxide  and 
will  absorb  this  gas  from  the  air,  becoming  potassium  carbonate. 
To  prevent  this,  a  layer  of  heavy  paraffine  oil  must  be  poured  upon 
the  surface  of  the  electrolyte. 

209.  The  Leclanche  Cell.— The  Leclanche  cell,  invented  in  1868, 
also  uses  a  solid  depolarizer.  From  its  cheapness,  simplicity  and 
freedom  from  dangerous  chemicals  it 
is  extremely  popular  and  in  one  form 
or  another  is  probably  more  used  than 
all  other  kinds  combined.  A  common 
form  is  shown  in  Fig.  103.  The  cell  is 
generally  a  glass  jar,  the  positive  ele- 
ment an  amalgamated  zinc  rod  placed 
in  one  corner  of  the  jar,  and  the  nega- 
tive plate  is  of  gas  carbon.  The  depolar- 
izer is  manganese  dioxide  used  in  the 
form  of  a  black  powder  and  the  many 
forms  of  this  cell  found  upon  the  market 
are  based  mainly  on  differences  in  the 
method  of  applying  the  depolarizer  to 
the  carbon  plate.  In  the  original  cell 
the  carbon  plate  was  placed  in  a  porous  Fig.  103. 

cup  which  was  then  packed  with  the 

powdered  depolarizer.  In  modern  forms  the  dioxide  may  be 
cemented  about  the  carbon  plate,  or  made  into  briquettes  and 
fastened  to  this  plate  by  rubber  bands,  or  may  even  be  com- 
pounded with  the  carbon  plate  itself.  Since  the  dioxide  is  a  poor 
conductor,  when  it  entirely  surrounds  the  carbon  plate  it  is  always 
mixed  with  powdered  carbon  by  which  its  resistance  is  reduced. 
The  electrolyte  is  a  solution  of  sal  ammoniac  (ammonium  chloride) 
and  the  reaction  when  the  circuit  is  closed  is 

Zn+2NH4Cl  =  ZnCl2+2NH3+H2 


166 


ELEMENTS  OF  ELECTRICITY. 


The  action  of  the  depolarizer  is 

H2 +2Mn02  =  H20  +Mn203 

Since  chemical  action  is  much  retarded  when  one  of  the  reagents 
is  in  the  form  of  a  solid,  the  depolarization  in  a  Leclanche  cell  does 
not  take  place  quickly  enough  to  consume  the  hydrogen  as  fast  as 
it  forms  and  the  cell  polarizes  rapidly.  However,  as  the  chemical 
action,  oxidizing  of  the  hydrogen,  keeps  on  steadily  after  the  cir- 
cuit is  broken,  the  cell  will  recover  after  a  short  rest.  These  cells 
are,  therefore,  not  fitted  to  supply  a  continuous  current  but  are 
admirably  adapted  for  intermittent  use  as  in  telephones,  door 
bells,  etc.  Their  electro-motive  force  is  about  1.4  volts,  there  is 
no  local  action  and  they  require  a  minimum  amount  of  attention. 

210.  Dry  Cells. — The  so-called  dry  cells,  in  common  use  in  this 
country,  are  in  principle  simply  Leclanche  cells  in  which  the  liquid 
has  been  reduced  to  a  minimum.  A  cross-section 
of  one  of  these  cells  is  shown  in  Fig.  104.  The 
cell  proper  is  a  zinc  can  which  serves  both  as  the 
cell  and  as  the  positive  plate.  The  negative 
plate  is  of  gas  carbon  and  may  be  corrugated  or 
fluted  so  as  to  expose  more  surface.  It  is  placed 
in  the  can  and  packed  around  with  a  mixture  of 
manganese  dioxide  and  granular  coke.  The 
packing  is  then  saturated  with  electrolyte,  usu- 
ally a  solution  of  zinc  chloride  and  ammonium 
chloride,  after  which  the  cell  is  sealed  with  a 
layer  of  pitch  or  asphalt.  This  serves  a  double 
purpose;  it  holds  the  carbon  plate  rigidly  in 
position  and  it  prevents  the  evaporation  of  the 
electrolyte.  To  secure  the  seal  more  firmly  a 
cannelure  or  groove  is  made  around  the  cell  near  the  top.  In 
some  of  these  cells  a  cementing  material  is  mixed  with  the  de- 
polarizer; in  others  the  can  is  lined  with  asbestus  or  with  paste- 
board which  has  been  soaked  with  the  electrolyte.  For  insulation, 
the  cell  is  usually  placed  in  an  outer  box  of  pasteboard. 

For  many  purposes  these  dry  cells  have  entirely  superseded  the 
wet  cells.  They  are  very  cheap,  costing  now  less  than  20  cents 
apiece,  and  for  average  door-bell  use  should  last  from  two  to  three 
years.  If  the  asphalt  seal  becomes  cracked,  they  soon  dry  out  and 
cease  to  act. 


Fig.  104. 


VOLTAIC  ELECTRICITY.  167 

211.  Need  of  Standard  Cells. — One  of  the  most  important 
classes  of  measurements  with  which  the  electrician  has  to  deal  is 
that  of  electro-motive  force.    In  Chapter  11  we  examined  electrom- 
eters, a  form  of  apparatus  sometimes  used  for  this  purpose,  and 
in  Chapter  34  we  shall  describe  voltmeters,  instruments  better 
adapted  for  practical  use  since  they  are  arranged  so  that  the  elec- 
tro-motive force  which  is  being  measured  can  be  read  direct  from 
a  printed  scale  without  the  necessity  of  resorting  to  intermediate 
calculations.    Even  the  best  instruments,  however,  do  occasion- 
ally get  out  of  adjustment  and  it  is  very  desirable  that  we  should 
possess  standards  of  electro-motive  force  by  which  our  instru- 
ments can  be  calibrated  in  the  first  place  and  compared  and  checked 
in  the  second.    While  the  average  E.  M.  F.  of  the  cells  described 
in  the  preceding  paragraphs  can  be  stated  with  considerable 
accuracy,  the  actual  E.  M.  F.  is  dependent  upon  varying  conditions 
and,  between  limits,  fluctuates  too  irregularly  and  with  too  much 
uncertainty  for  these  cells  to  be  used  as  standards.     However, 
there  have  been  devised  certain  "standard  cells"  in  which  the 
variable  factors,  except  that  of  temperature,  have  been  eliminated 
and  the  temperature  coefficient,  or  change  of  E.  M.  F.  with  tem- 
perature, determined.    These  cells  are  used  for  their  E.  M.  F.  and 
not  to  supply  current  and  since  the  E.  M.  F.  is  independent  of  the 
size  of  the  cells  (Par.  200),  they  are  made  very  small,  some,  in  fact, 
being  hardly  larger  than  a  thimble.    Analogous  to  this  would  be 
the  use  of  vertical  columns  of  water  as  standards  of  pressure. 
Since  hydrostatic  pressure  per  unit  area  is  dependent  upon  the 
height  of  the  column  and  is  independent  of  its  cross-section,  and 
since  no  current  or  flow  of  water  is  required,  these  vertical  columns 
could  be  contained  in  slender  tubes. 

212.  Clark's  Standard  Cell.— In  1893  the  International  Con- 
gress of  Electricians  in  session  in  Chicago  passed  resolutions  defin- 
ing certain  electrical  units  upon  which  at  that  time  the  scientific 
world  was  not  universally  agreed.    These  definitions  were  formally 
legalized  by  Act  of  Congress,  approved  July  12,  1894.    Among 
others,  there  was  defined  the  unit  of  electro-motive  force,  the  inter- 
national volt,  and  to  the  definition  proper  was  added  that  it  was 
"represented  sufficiently  well  for  practical  use  by  1|§£  of  the  elec- 
tro-motive force  between  the  poles  of  the  voltaic  cell,  known  as 
Clark's  cell,  at  a  temperature  of  15°  C  and  prepared  in  the  manner 
described  in  the  accompanying  specification." 


168 


ELEMENTS  OF  ELECTRICITY. 


There  are  a  number  of  forms  of  this  cell.  The  one  shown  in  Fig. 
105  is  in  accordance  with  the  specification  referred  to.  The  cell 
proper  is  a  two-limbed  bottle  closed  with  a  ground-glass  stopper. 
Through  the  bottom  of  each  limb  there  is  fused  a  fine  platinum 
wire,  the  two  serving  as  the  terminals  of  the  cell.  In  principle, 

the  cell  is  the  same  as  Daniell's. 
The  positive  plate  is  amalgamated 
zinc,  the  negative  plate  is  mercury, 
the  electrolyte  is  a  solution  of  zinc 
sulphate  and  the  depolarizer  is 
mercurous  sulphate.  The  zinc  a- 
malgam  is  composed  of  nine  parts 
of  mercury  and  one  of  zinc,  and  is 
liquid  at  the  temperature  of  boil- 
ing water  but  sets  at  ordinary 
temperatures.  It  is  melted  and 
poured  into  one  of  the  limbs. 
Upon  this  is  packed  a  half-inch 
layer  of  crystals  of  zinc  sulphate. 
In  the  other  limb  is  poured  per- 
fectly pure  mercury,  then  on  top 
of  this  a  layer  of  mercurous  and 
zinc  sulphates  worked  up  together 

into  a  paste,  and  on  top  of  this  paste  a  half-inch  layer  of  the 
crystals  of  zinc  sulphate.  Finally,  the  bottle  is  filled  to  the  neck 
with  a  saturated  solution  of  zinc  sulphate  and  the  stopper  is 
cemented  in  with  shellac,  leaving  beneath  it  a  small  air  bubble  to 
allow  for  expansion  of  the  liquid  with  changes  of  temperature. 
The  cell  is  then  placed  in  a  protecting  outer  case,  the  wires  being 
brought  out  to  suitable  binding  posts,  and  an  opening  is  left  in  the 
cover  through  which  a  thermometer  may  be  inserted  to  take  the 
temperature  of  the  cell. 

The  chemical  action  is  similar  to  that  given  for  Daniell's  cell 
(Par.  206). 


SATURATED  SOLUTION 
OF  XINC  SULPHATE 


Fig.  105. 


the  S04  attacking 

the  zinc  of  the  positive  plate,  the  Hg2  coalescing  with  the  mercury 
of  the  negative  plate  and  there  thus  being  no  polarization. 

The  E.  M.  F.  of  a  Clark  cell  at  15°  C  (59°  F)  is  1.434  volts  and 


VOLTAIC  ELECTRICITY.  169 

its  temperature  coefficient  or  change  of  E.  M.  F.  per  degree  Centi- 
grade is  about  .00115.  This  is  negative,  that  is,  the  E.  M.  F. 
decreases  as  the  temperature  increases.  At  50°  T  it  is  1.440;  at 
80°  F  it  is  1.421.  This  change  in  E.  M.  F.  with  change  in  tempera- 
ture is  due  to  corresponding  change  in  solubility  of  zinc  sulphate 
and  hence  variation  in  the  density  of  the  electrolyte.  The  exact 
E.  M.  F.  at  any  temperature  t  Centigrade  is  given  by  the  formula 

Et  =  1.434 -.00119  (Z-15) -.000007  (Z-15)2 

213.  Western's  Standard  Cell.— The  Weston  standard  cell  is 
in  principle  precisely  the  same  as  the  Clark  cell,  cadmium  being 
substituted  for  zinc,  that  is,  the  positive  plate  being  a  cadmium 
amalgam,  the  electrolyte  being  a  saturated  solution  of  cadmium 
sulphate,  etc.,  and  the  mechanical  arrangement  being  similar  to 
that  just  described.     Since  the  solubility  of  cadmium  sulphate 
varies  but  little  with  temperature,  the  temperature  coefficient  is 
very  small,  being  only  .00004  volt  per  degree  Centigrade.    For  all 
ordinary  purposes,  this  change  may  be 

neglected  and  the  E.  M.  F.  of  the  cell 
may  be  taken  as  1.019  volts. 

214.  Conventional    Sign    for   Cell.  - 
Since  in  the  study  of  electricity  it  often 
becomes  necessary  to  make  diagrams  in 
which  cells  appear,  a  conventional  sign 
for  the  same  has  been  adopted.    In  Fig. 

106,  a  represents  the  plan  of  two  cells  k 

connected  together  and  b  represents  the  Fig  106 

conventional  sign  for  the  same  two  cells. 

In  both,  the  short  heavy  line  represents  the  zinc,  the  long  thin 
line  the  copper.  It  will  be  noted  that  in  the  conventional  sign 
the  cell  itself  is  omitted  as  well  as  the  connecting  wire  between 
the  cells. 


170  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  21. 

THE   ELECTRIC   CURRENT   AND   ITS   CHEMICAL 
ACTION. 

215.  Electric  Current. — In  Par."  70  it  was  stated  that  when 
conductors  at  different  potentials  are  brought  into  contact  (either 
directly  or  through  a  third  conducting  body),  there  is  a  flow  of 
positive  electricity  from  the  one  of  higher  potential  to  that  of 
lower.    Again,  in  Par.  75  it  was  stated  that  if  new  charges  were 
supplied  to  the  body  of  higher  potential  as  fast  as  the  preceding 
charges  flowed  away,  then  the  body  would  be  maintained  at  a 
constant   potential   and   the   successive   charges   flowing  away 
would  constitute  a  continuous  stream  or  current.     Such  is  the 
state  of  affairs  in  a  voltaic  cell.    The  chemical  action  at  the  surface 
of  the  zinc  plate  produces  fresh  quantities  of  electricity  as  fast  as 
those  previously  produced  flow  away.    These  successive  charges 
pass  across  to  the  copper  plate  and  raise  its  potential,  and  if  this 
copper  plate  be  connected  by  a  wire  to  the  zinc  plate  a  current 
will  flow  through  the  wire.    It  must,  however,  be  borne  in  mind 
that  electricity  is  not  matter  and  that  there  is  no  actual  movement 
of  material  substance.     Nevertheless,  we  do  know  that  when 
points  at  different  potentials  are  connected  by  a  conductor,  certain 
perceptible  effects  are  produced  along  this  conductor;  among 
them  (a)  the  temperature  of  the  conductor  rises,  (b)  a  magnetic 
field  is  established  about  this  conductor  and  (c)  if  a  part  of  the 
conducting  path  lies  through  a  chemical  compound,  chemical 
decomposition  will  generally  ensue.     We  are  agreed  then  that 
when  these  phenomena  occur,  a  current  is  flowing  through  the 
conductor.    The  terms  "current,"  "flow/'  etc.,  are  survivors  of 
the  time  when  electricity  was  spoken  of  and  regarded  as  a  fluid, 
and  being  such  convenient  forms  of  expression  they  are  retained. 

216.  No  Current  Unless  Circuit  be  Complete. — The  path  over 
which  the  current  flows  is  called  the  circuit.    There  can  be  no  flow 
unless  this  circuit  be  complete,  that  is,  unless  there  be  a  continuous 
conducting  path  from  the  surface  at  which  the  current  originates 


VOLTAIC  ELECTRICITY.  171 

back  to  the  other  side  of  this  surface.  Thus,  in  a  simple  cell,  con- 
sidering the  surface  of  the  zinc  as  a  layer  of  appreciable  thickness, 
the  current  originates  at  the  outer  part  of  this  layer  where  it  is  in 
contact  with  the  electrolyte,  then  traverses  the  electrolyte  to  the 
copper  plate,  thence  out  upon  the  wire  and  back  to  the  zinc  plate 
and  finally  down  this  plate  to  the  inner  side  of  the  layer.  If  the 
circuit  be  continuous  it  is  said  to  be  closed;  if  it  be  not  continuous 
it  is  said  to  be  broken  or  open.  Since  the  current  thus  returns  upon 
itself,  it  is  analogous  to  water  which  entirely  fills  a  pipe  bent 
around  into  the  form  of  a  ring.  If  this  water  be  put  in  motion  it 
can  be  checked  by  closing  a  cock  in  the  pipe  at  any  point  whatso- 
ever. So  the  electric  current  is  stopped  by  breaking  the  circuit  at 
any  point  at  all. 

217.  Direction  of  Flow  of  Current. — We  assume  the  current  to 
flow  from  a  higher  potential  to  a  lower,  but  (Par.  27)  which  poten- 
tial is  high  and  which  is  low  is  itself  purely  a  matter  of  convention, 
therefore,  even  admitting  that  there  is  a  flow,  we  have  no-  way  of 
determining  in  which  direction  it  actually  takes  place.    At  first 
sight  it  seems  that  we  could  easily  determine  this  direction.    Sup- 
pose we  have  a  cell  operating  an  electric  bell  at  some  distance;  the 
energy  must  surely  have  originated  in  the  cell  and  moved  out 
along  the  wire  to  the  bell.    But,  from  the  preceding  paragraph, 
there  can  be  no  current  unless  there  be  a  complete  circuit,  hence 
there  must  be  two  wires  or  paths  from  the  cell  to  the  bell  and  we 
have  no  way  of  discovering  upon  which  of  the  two  the  current 
moved  out. 

Notwithstanding  the  foregoing,  some  of  the  phenomena  pro- 
duced by  the  current  do  have  direction  with  respect  to  the  assumed 
direction  of  flow.  The  heating  effect  of  the  current  in  a  homo- 
geneous conductor  is  irrespective  of  the  direction  of  flow,  but  the 
direction  of  the  magnetic  field  about  the  conductor  and  the  direc- 
tion in  which  the  products  of  electro-chemical  decomposition 
move  are  dependent  upon  this  flow  and  are  reversed  when  the 
direction  of  the  current  is  reversed. 

218.  Decomposition   of   Water.— On   March  20,   1800,   Volta 
addressed  to  Sir  Joseph  Banks  of  the  Royal  Society  of  London  a 
portion  of  a  letter  describing  the  Voltaic  Pile.    This  letter  was  not 
communicated  to  the  Society  until  some  time  in  June  when  the 
remainder  had  been  received,  but  in  the  mean  time  it  had  been 


172 


ELEMENTS  OF  ELECTRICITY. 


shown  to  two  of  the  members,  Carlisle  and  Nicholson.  Wishing 
to  test  the  apparatus,  they  extemporized  one  with  seventeen  silver 
coins,  an  equal  number  of  copper  discs  and  pieces  of  cloth  soaked 
in  a  weak  solution  of  common  salt.  In  order  to  make  good  con- 
nection with  a  metal  plate  which  they  were  endeavoring  to  charge, 
they  placed  upon  it  a  drop  of  water  and  inserted  in  this  drop  the 
end  of  one  of  the  wires  from  the  pile.  At  once  fine  bubbles  rose 
in  the  liquid.  Continuing  these  investigations,  Nicholson  within 
the  next  few  days  devised  another  experiment.  He  inserted  in 
one  end  of  a  glass  tube  a  cork,  poured  some  water  into  the  tube 
and  then  corked  the  other  end.  Through  each  of  these  corks  he 
then  thrust  a  platinum  wire  so  that  the  ends  protruded  some  dis- 
tance into  the  water.  When  these  wires  were 
connected  to  the  extremities  of  the  pile,  streams 
of  bubbles  were  given  off  from  each  of  the  ends, 
and  when  tested  separately,  it  was  found  that 
oxygen  was  released  at  the  wire  by  which  the 
current  entered  the  water  and  hydrogen  at  the 
wire  by  which  it  left. 

219.  Electrolysis  of  Water. — This  decompo- 
sition produced  by  the  electric  current  is  called 
"electrolysis"  i.  e.,  electric  analysis.  The  elec- 
trolysis of  water  can  best  be  studied  by  means 
of  the  apparatus  shown  in  Fig.  107.  This  con- 
sists of  three  glass  tubes  connected  as  shown. 
The  tubes  H  and  0  are  burettes  graduated  in 
cubic  centimeters,  usually  to  the  nearest  tenth, 
the  graduations  reading  from  the  top  down- 
ward. Through  the  bottom  of  these  burettes 
there  are  sealed  the  platinum  wires  A  and  B 
terminating  on  the  inside  in  the  platinum  plates 
C  and  D.  The  third  tube  is  expanded  at  the 
top  into  the  reservoir  R  which  is  at  a  higher 
level  than  the  tips  of  the  burettes.  The  apparatus  is  supported 
on  a  suitable  stand.  With  the  stop  cocks  H  and  0  open,  water, 
to  which  a  few  drops  of  sulphuric  acid  have  been  added,  is  poured 
into  R.  The  liquid  rises  in  the  burettes  and  the  stop  cocks  are 
closed  as  soon  as  its  level  passes  them.  The  addition  of  the 
sulphuric  acid  is  usually  explained  by  the  statement  that  it  is 
used  merely  to  improve  the  conducting  power  of  the  water. 


Fig.  107. 


VOLTAIC  ELECTRICITY.  173 

Perfectly  pure  water  is  a  non-conductor,  and  the  acidulated 
water  does  conduct,  but  the  true  reason  for  the  use  of  the  acid 
is  given  below.  If  a  current  be  now  brought  in  at  A  and  out 
at  J5,  bubbles  will  rise  from  the  plates  C  and  D  and  collect  in 
the  upper  parts  of  the  burettes,  pushing  down  the  liquid  which 
will  rise  in  the  reservoir.  The  gas  in  0  will  be  found  to  be  oxygen 
and  that  in  H,  hydrogen;  furthermore,  the  amount  of  gas  generated 
in  H  will  be  very  nearly  twice  that  generated  in  0.  The  volume 
of  the  hydrogen  would  be  exactly  twice  that  of  the  oxygen  were 
it  not  for  the  facts  that  (a)  some  of  the  oxygen  is  given  off  in  the 
denser  form  of  ozone,  (b)  some  of  each  gas,  but  not  proportional 
amounts,  is  dissolved  in  the  water,  (c)  a  portion  of  the  gases  is  oc- 
cluded by  the  platinum  plates  and  (d)  owing  to  the  difference  of  the 
levels  of  the  water  in  the  two  burettes,  the  hydrogen  is  under 
greater  hydrostatic  pressure  than  is  the  oxygen. 

The  chemical  action  is  usually  explained  by  saying  that  the 
water  is  decomposed  into  its  component  gases  hydrogen  and 
oxygen,  and  this  is  correct  but  it  is  not  the  primary  reaction  which 
takes  place.  The  sulphuric  acid  is  first  separated  into  H2  and  SO  4, 
the  hydrogen  being  released  and  the  SO  4  then  attacking  the  water, 
thus 


so  that  the  oxygen  is 
released  as  the  result  of  a  secondary  reaction. 

220.  Faraday's  Terminology.  —  The  decomposition  of  chemical 
compounds  by  the  electric  current  was  investigated  by  Faraday 
to  whom  is  due  the  terminology  now  employed.     As  we  have 
already  seen,  the  liquid  which  undergoes  decomposition  is  called 
the  electrolyte  and  the  process  itself  is  electrolysis.    The  vessel  in 
which  electrolysis  takes  place  is  called  an  electrolytic  cell.    The 
plates  or  wires  which  dip  into  the  liquid  and  by  which  the  current 
is  brought  in  and  taken  out  are  termed  collectively  the  electrodes; 
that  by  which  the  current  enters  is  the  anode;  that  by  which  it 
leaves  is  the  cathode.    The  part  molecules  into  which  the  substance 
being  decomposed  is  split  are,  in  allusion  to  their  movement 
through  the  liquid,  called  ions  (wanderers)  ;  those  which  appear  at 
the  anode  are  anions;  those  released  at  the  cathode  are  cathions 
or  kations. 

221.  Substances    Subject   to   Electrolysis.  —  In   order   that   a 
substance  may  be  electrolyzed  it  must  fulfill  the  following  condi- 


174  ELEMENTS  OF  ELECTRICITY. 

tions;  it  must  be  a  compound  substance;  it  must  be  a  conductor; 
it  must  be  in  a  liquid  state,  either  as  the  result  of  fusion  or  of 
solution.  Mercury  and  the  fused  metals  are  conducting  liquids 
but  being  elementary  bodies  can  not  be  decomposed.  All  other 
conducting  liquids  undergo  electrolysis. 

222.  Electrolysis  of  a  Fused  Compound. — The  electrolysis  of 
lead  chloride  may  be  taken  as  an  example  of  the  decomposition 
of  a  fused  compound.    The  salt  is  kept  in  a  molten  state  in  a  small 
porcelain  crucible  placed  over  a  bunsen  burner.    The  electrodes 
of  iron  dip  into  the  fused  mass.    When  a  current  passes,  chlorine 
is  liberated  at  the  anode,  as  may  be  shown  by  the  bleaching  effect 
upon  a  piece  of  litmus  paper  held  just  above,  and  lead  is  released 
at  the  cathode. 

223.  Electrolysis  of  a  Base. — In  many  cases  of  electrolysis  the 
primary  reactions  are  obscured  by  the  secondary.     In  the  elec- 
trolysis of  water  (Par.  219),  it  is  really  the  sulphuric  acid  that  is 
electrolyzed,  the  decomposition  of  the  water  being  the  result  of 
secondary  reactions.    Similar  results  follow  the  electrolysis  of  the 
strong  bases.     For  example,  a  solution  of  potassium  hydroxide 
electrolyzes  as  follows: 

2KOH  =  K2+H20+0 

the  oxygen  appearing 

at  the  anode  and  the  potassium  being  released  at  the  cathode,  but 
as  soon  as  this  metal  is  released  it  attacks  the  water,  thus 

K+2H20=2KOH+H2 

*SALJ  so  that  the  net 

result  is  the  same  as  when  sulpflunc  acid  is  electrolyzed,  that  is, 
the  water  is  decomposed.  If,  however,  the  cathode  be  of  mercury, 
the  potassium  amalgamates  with  it  and  by  distilling  off  the  mer- 
cury from  the  amalgam  the  potassium  may  be  separated  and  col- 
lected. In  a  somewhat  similar  manner  to  this,  Davy  discovered 
in  October,  1807,  first  potassium  and  rapidly  thereafter  sodium 
and  other  alkaline  and  alkaline-earth  metals. 

224.  Electrolysis  of  a  Metallic  Salt. — When  a  metallic  salt  in 
solution  is  electrolyzed,  the  metal  appears  at  the  cathode,  the  acid 
radicle  at  the  anode,  but,  as  mentioned  above,  this  primary  re- 
action is  frequently  obscured  by  secondary  reactions. 

In  the  electrolysis  of  an  alkali  oxy-salt,  these  secondary  reactions 


VOLTAIC  ELECTRICITY.  175 

occur  at  both  anode  and  cathode.  For  example,  if  sodium  sulphate 
be  electrolyzed  the  sodium  is  released  at  the  cathode  but  imme- 
diately reacts  with  the  water  releasing  hydrogen.  The  SO  4  is 
released  at  the  anode  and,  as  described  above,  reacts  with  the 
water  releasing  oxygen.  The  net  result  therefore  is  simply  the 
electrolysis  of  the  water. 

If  a  solution  of  copper  sulphate  be  electrolyzed  the  copper  is 
deposited  upon  the  cathode  and  the  S04  is  released  at  the  anode 
where  one  of  two  effects  may  be  produced  according  as  the  anode 
is  or  is  not  attacked  by  the  S04.  If  the  anode  be  of  platinum,  the 
SO  4  attacks  the  water,  forming  sulphuric  acid  and  releasing 
oxygen.  If,  however,  the  anode  be  of  copper,  the  S04  attacks  it, 
producing  copper  sulphate  which  goes  into  solution.  As  fast  as 
copper  is  deposited  upon  the  cathode,  an  equal  amount  is  dissolved 
from  the  anode;  the  electrolyte  therefore  remains  of  constant 
strength.  This  is  true  for  other  metals  than  copper.  If  a  salt  -of  a 
metal  be  electrolyzed  between  electrodes  of  that  metal,  the  anode 
wastes  away,  the  cathode  increases  and  the  electrolyte  remains  of 
constant  concentration. 

The  metals,  which  in  the  above  are  said  to  be  released  at  the 
cathode,  are  really  deposited  upon  the  cathode  in  a  compact  and 
tightly  adhering  layer.  This  is  the  basis  of  the  important  proc- 
esses of  electroplating  and  electrotyping  to  be  described  later. 
Electrolysis  has  many  other  important  applications,  such  as  the 
electrolytic  refining  of  copper,  the  manufacture  of  chlorine,  of  the 
alkaline  hydroxides,  of  aluminum,  etching  on  metal,  photo-en- 
graving, etc. 

225.  Electro-Chemical  Classification  of  the  Elements.— The 
elements  have  been  classed  according  to  their  behaviour  under 
electrolysis.  Those  which  move  in  the  direction  of  the  current  and 
are  released  at  the  cathode  are  called  electro-positive,  this  name 
being  given  because  they  move  to  the  negative  plate.  Those  which 
move  against  the  current  and  appear  at  the  anode  or  positive  plate 
are  called  electro-negative.  Hydrogen  and  the  metals  are  electro- 
positive; the  non-metals  are  electro-negative.  It  will  be  noted 
that  in  its  electro-chemical  behaviour  hydrogen  conforms  to  its 
purely  chemical  behaviour  and  arranges  itself  with  the  metals. 
The  above  classification,  which  is  also  extended  to  compound  ions, 
is  not  absolute;  an  element  in  certain  compounds  being  electro- 
positive, while  in  others  it  may  be  electro-negative. 


176  ELEMENTS  OF  ELECTRICITY. 

226.  Faraday's  First  Law. — It  was  stated  above  (Par.  215)  that 
when  an  electric  current  is  flowing  there  is  no  material  substance 
in  movement  but  there  is  a  transfer  of  energy  which  manifests 
itself  in  the  production  of  heat,  of  magnetic  effects,  and  of  chemical 
decomposition.    It  is  a  known  fact  that  the  same  amount  of  chem- 
ical action  always  produces  the  same  amount  of  energy  and,  con- 
versely, the  same  expenditure  of  energy  in  the  production  of 
chemical  decomposition  always  brings  about  the  same  amount. 
The  truth  of  this  was  recognized  by  Faraday,  the  first  to  investi- 
gate the  laws  of  electrolysis,  and  was  formulated  by  him  to  the 
effect  that  the  amount  of  chemical  action  produced  in  an  electrolytic 
cell  is  proportional  to  the  quantity  of  electricity  which  flows  through 
the  cell.    The  amount  of  chemical  action  produced  by  the  passage 
of  an  electric  current  may  therefore  be  taken  as  a  measure  of  the 
quantity  transferred. 

227.  Voltameters. — An    electrolytic    cell    so    made    that    the 
chemical   action   produced   by   the   current   can   be   accurately 
measured,  and  hence  the  current  determined,  is  called  a  voltameter. 
Voltameters  are  arranged  so  that  the  metal  (usually  silver  or 
copper),  deposited  upon  the  cathode  may  be  weighed,  or  the 
amount  of  gas  released  may  be  measured  and  its  weight  calculated. 
The  latter  class,  the  gas  voltameters,  may  collect  the  gases  sepa- 
rately, as  shown  in  Fig.  107,  or  may  gather  these  gases  in  a  common 
burette  thereby  obtaining  a  greater  volume  for  measurement. 

We  shall  shortly  see  that  there  is  another  instrument,  a  volt- 
meter, used  for  quite  a  different  purpose,  the  measurement  of 
electro-motive  force.  It  is  unfortunate  that  these  names  are  so 
much  alike  and  the  beginner  must  be  on  his  guard  not  to  confound 
the  two. 

228.  The  Coulomb  and  the  Ampere. — To  define  a  current  of 
water,  it  is  not  sufficient  to  state  the  amount  of  water  which  will 
flow  past  a  certain  point  but  we  must  also  state  the  rate  at  which 
it  flows  past.    So  also  with  the  electric  current;  we  must  know  both 
the  quantity  and  the  rate  at  which  this  quantity  is  delivered. 

The  practical  unit  of  electrical  quantity,  the  coulomb,  is  defined  as 
that  quantity  of  electricity  which  flowing  through  a  gas  volta- 
meter liberates  .00001035+  of  a  gram  of  hydrogen. 

Now,  a  very  feeble  current  must  flow  a  long  time  to  accom- 
plish the  same  amount  of  chemical  work  as  a  current  of  greater 


VOLTAIC  ELECTRICITY.  177 

strength;  on  the  other  hand,  the  greater  the  current,  the  greater 
the  amount  of  work  done  in  a  given  time.  We  can  therefore  com- 
pare currents  by  comparing  the  amount  of  chemical  work  done  in 
a  given  time.  The  practical  unit  of  current,  the  ampere,  is  defined 
as  that  unvarying  current  which  flowing  through  a  gas  voltameter 
liberates  .00001035+  of  a  gram  of  hydrogen  per  second.  Why  this 
particular  weight  was  selected  will  be  explained  later  (Pars.  231, 
232,  450).  From  the  foregoing,  it  is  seen  that  a  current  of  one 
ampere  delivers  one  coulomb  per  second,  or  that  if  Q  be  the  number 
of  coulombs,  /  be  the  current  in  amperes,  and  t  be  the  time  in 
seconds,  then 

Q=It 

This  may  also  be  written  I=Q/t,  whence  we  see  that  the  cur- 
rent in  amperes  is  equal  to  the  rate  at  which  coulombs  are  de- 
livered, or  the  number  of  coulombs  per  second. 

The  unit  of  quantity,  the  coulomb,  must  not  be  confused  with 
the  electro-static  unit  of  quantity  as  defined  in  Par.  56.  The 
coulombjs  equal  to  very  nearly  3  XlO9  or  three  billion  of  the  elec- 
trostatic units. 

With  practical  experience  in  the  Laboratory,  the  student  will 
soon  form  a  conception  of  the  ampere  which  at  first  must  be  to 
him  more  or  less  of  an  abstraction.  The  current  employed  in  the 
16  candle  power  110  volt  incandescent  lamp  is  about  one-half 
ampere. 

In  solving  ordinary  problems  given  for  practice,  it  is  sufficiently 
accurate  to  take  the  amount  of  hydrogen  released  by  one  coulomb 
as  .00001  (one  one-hundred  thousandth)  of  a  gram. 

229.  Equality  of  Current  at  Every  Cross-Section  of  a  Circuit. — 

At  every  cross-section  of  a  circuit  through  which  a  current  is 
flowing,  the  current  is  the  same.  This  is  a  simple  principle  but 
often  confuses  the  beginner  who  has  a  tendency  to  suppose  that  a 
current  may  start  out  of  a  certain  strength  but  may  be  used  up 
and  dwindle  away  as  it  progresses  around  the  circuit.  The  current 
may  be  compared  to  water  which  completely  fills  a  pipe  bent  into 
the  shape  of  a  ring.  No  water  can  move  at  any  point  unless 
exactly  the  same  amount  moves  at  every  other  cross-section  of  the 
pipe. 

A  corollary  following  directly  from  the  above  is  that  the  amount 
of  chemical  action  at  every  cross-section  of  a  circuit  is  the  same. 


178 


ELEMENTS  OF  ELECTRICITY. 


This  may  be  shown  experimentally  as  follows.  In  Fig.  108,  A 
represents  a  battery  of  Daniell  cells  connected  one  after  the  other, 
or  in  series  (three  are  represented  in  the  diagram  but  as  many  as 
may  be  necessary  are  used),  and  B,  C,  D,  and  E  represent  copper 
voltameters.  When  the  key  K  is  closed,  completing  the  circuit, 
a  current  flows  through  the  battery,  through  B,  then  divides,  part 
going  through  C  and  the  rest  through  D,  then  reunites,  passes 
through  E  and  back  to  the  negative  pole  of  the  battery.  Before 


Fig.  108. 

closing  the  key,  the  cathodes  of  the  voltameters  and  of  each  of  the 
Daniell  cells  are  carefully  weighed.  After  the  current  has  flowed 
for  a  while,  the  key  is  opened,  stopping  the  current,  and  the 
cathodes  are  removed,  dried,  and  carefully  reweighed.  They  are 
all  found  to  have  increased  in  weight,  the  increase  being  exactly 
the  same  in  all  except  C  and  D  and  in  these  their  joint  increase 
being  equal  to  the  increase  in  each  of  the  other  cathodes.  It  is  to 
be  especially  noted  that  the  amount  of  chemical  action  is  also  the 
same  in  every  one  of  the  battery  cells  in  series. 

230.  Faraday's  Second  Law. —  Suppose  we  arrange  a  similar 
experiment  with  a  number  of  voltameters  in  series  but  each  con- 
taining different  compounds.  Suppose  one  to  be  a  gas  voltameter, 
one  to  contain  a  solution  of  silver  nitrate,  one  of  copper  sulphate, 
one  of  cuprous  chloride  and  one  of  tin  tetra-chloride.  If  now  the 
key  be  closed,  the  same  current  will  traverse  them  all.  After  the 
current  has  flowed  for  a  while,  open  the  key,  remove  and  weigh 
the  cathodes  and  measure  and  calculate  the  weight  of  the  hydrogen 
evolved  in  the  gas  voltameter.  If  we  take  the  weight  of  this 
hydrogen  as  unity  we  will  find  that  107.9  parts  of  silver,  31.8  parts 
of  copper  in  the  copper  sulphate  solution,  63.6  parts  in  the  cuprous 
chloride  solution  and  29.8  parts  of  tin  have  been  deposited.  But 


VOLTAIC  ELECTRICITY.  179 

these  numbers,  107.9,  31.8,  63.6,  and  29.8  are  the  equivalent 
weights  of  the  corresponding  elements  in  the  respective  compounds. 
(The  equivalent  weight  of  an  element  or  of  a  radicle  is  defined  as 
that  weight  of  it  which  combines  with  or  displaces  or  is  chemically 
equal  to  one  part  by  weight  of  hydrogen.  It  may  be  obtained  by 
dividing  the  atomic  weight  of  the  element,  or  the  molecular  weight 
of  the  radicle,  by  the  valency  which  it  has  in  the  compound  under 
consideration.)  The  foregoing  results  are  expressed  in  Faraday's 
second  law  which  is  to  the  effect  that  the  weights  of  the  ions  of 
different  substances  liberated  by  the  same  quantity  of  electricity 
are  to  each  other  as  the  equivalent  weights  of  these  ions. 

231.  Electro -Chemical  Equivalent. — The  electro-chemical  equiv- 
alent of  an  element  is  the  weight  in  grams  of  that  element 
liberated  by  one  coulomb.    By  definition  (Par.  228)  one  coulomb 
liberates  .00001035+  of  a  gram  of  hydrogen,  which  is  therefore 
its  electro-chemical  equivalent.    The  electro-chemical  equivalent 
of  any  other  element  is  obtained  by  multiplying  its  equivalent 
weight  by  this  electro-chemical  equivalent  of  hydrogen.     For 
example,  for  silver  it  is  107.93 X. 00001035+  =.001118,  and  for 
copper  it  is  .000328. 

To  liberate  one  gram  of  hydrogen  (about  four-tenths  of  a  cubic 
foot  at  ordinary  temperature)  requires  1/.00001035+,  or,  in 
round  numbers,  96,540  coulombs.  This  would  require  a  current 
of  one  ampere  to  flow  for  nearly  27  hours.  This  quantity  of  elec- 
tricity, 96,540  coulombs,  will  release  one  gram-equivalent  of  any 
ion,  as  for  example  8  grams  of  oxygen,  107.93  grams  of  silver,  etc. 

From  the  foregoing,  it  is  seen  that  to  find  the  weight  of  any  ion 
released  by  a  given  current  in  a  given  time,  we  determine  the  num- 
ber of  coulombs  and  multiply  this  number  by  the  electro-chemical 
equivalent  of  the  ion. 

232.  Definition  of  the  Ampere  in  Terms  of  Silver.— For  prac- 
tical purposes,  because  of  the  difficulty  of  handling  and  weighing 
a  gas,  it  is  desirable  to  have  the  ampere  defined  in  terms  of  some 
solid  element  instead  of  hydrogen.    Silver  is  found  to  be  the  most 
suitable  and  copper  the  next.    In  the  preceding  paragraph  we  have 
seen  that  the  electro-chemical  equivalent  of  silver,  the  weight 
deposited  by  one  coulomb,  or  one  ampere  flowing  for  one  second, 
is  .001118  gram.     The  International  Congress  of  Electricians 
of  1893  in  the  resolutions  already  referred  to  (Par.  212),  accord- 


180  ELEMENTS  OF  ELECTRICITY. 

ingly  defined  the  ampere  as  that  unit  "which  is  represented  suf- 
ficiently well  for  practical  use  by  the  unvarying  current  which 
when  passed  through  a  solution  of  nitrate  of  silver  in  water,  in 
accordance  with  the  accompanying  specification,  deposits  silver 
at  the  rate  of  .001118  gramme  per  second." 

233.  Applications  of  Electrolysis,  Refining  of  Copper. — Copper 
as  it  comes  from  the  smelter  may  contain  impurities  of  two  kinds, 
first,  objectionable  substances  such  as  arsenic,  antimony,  etc., 
which  injure  its  ductility  and  its  electrical  properties  and,  second, 
small  amounts  of  gold  and  silver  which  it  is  desirable  to  recover 
if  possible.    The  impure  copper  is  cast  into  slabs  which  are  used 
as  the  anodes  in  large  electrolytic  tanks,  the  electrolyte  being  a 
solution  of  copper  sulphate  and  the  cathodes  being  thin  sheets  of 
pure  copper.    As  the  current  passes,  the  anode  is  eaten  away,  the 
pure  copper  being  deposited  upon  the  cathode  and  the  impurities 
settling  as  a  slime  to  the  bottom  of  the  tank  whence  they  are 
removed  from  time  to  time  and  treated  according  to  their  value. 
If  the  impure  copper  contains  much  gold  or  silver,  the  anodes  may 
be  enclosed  in  canvas  bags  which  permit  the  free  passage  of  the 
solution  but  catch  the  slime  which  falls.    The  copper  is  refined  at 
the  rate  of  about  seven  pounds  per  hour  per  horse-power  expended. 

234.  Electroplating. — The  object  to  be  plated  is  immersed  in 
the  electrolyte  and  serves  as  the  cathode.     In  gold  and  silver 
plating,  the  anode  is  a  plate  of  the  desired  metal  and  the  electrolyte 
is  a  double  cyanide  of  potassium  and  this  metal.    The  deposits 
from  these  cyanides  are  smoother  and  more  compact  than  those 
from  other  salts.    There  must  be  a  certain  relation  between  the 
current  and  the  area  of  the  surface  to  be  plated.    If  the  current  be 
too  great,  the  deposit  is  granular  or  coarsely  crystalline  and  may 
not  adhere.    Portions  of  the  surface  which  are  not  to  be  plated 
may  be  covered  with  a  coating  of  wax  or  varnish. 

235.  Electrotyping. — The  process  of  electrotyping  is  employed 
to  obtain  exact  reproductions  of  wood  cuts,  engraved  plates, 
forms  of  set  type,  etc.    The  need  for  such  reproductions  is  readily 
understood.    If  impressions  be  taken  direct  from  a  wood  cut  it 
rapidly  wears  away  and  frequently  gives  out  when  about  5000 
have  been  struck  off.    By  electrotyping,  a  reproduction  of  the  cut 
can  be  made  in  copper  and  this  reproduction  can  be  used  many 
thousand  times  and  as  many  others  may  be  made  as  desired,  the 


VOLTAIC  ELECTRICITY.  181 

original  cut  not  suffering  in  the  slightest.  Again,  a  great  many 
million  postage  stamps  are  printed  annually  by  the  Government 
and  not  only  must  they  be  struck  off  several  hundred  in  a  sheet 
but  several  presses  must  be  running  at  the  same  time.  If  each 
plate  had  to  be  engraved  separately  the  cost  would  be  tremendous 
and  no  two  stamps  on  a  sheet  would  be  exactly  alike.  However, 
the  engraver  prepares  a  plate  for  a  single  stamp  and  hundreds  of 
reproductions  can  be  made  and  these  reproductions  can  then  be 
united  in  one  large  plate.  Finally,  when  type  have  been  set  for  a 
printed  page  they  are  withdrawn  from  the  printer's  stock.  Should 
this  run  low,  he  must  either  purchase  more  or  distribute  those 
which  have  been  set  up,  thus  undoing  the  work.  However,  by 
electrotyping  he  can  reproduce  the  entire  page  in  one  piece  and  the 
type  then  become  available  for  other  use. 

The  process  consists  in  pressing  the  cut  or  type  to  be  reproduced 
into  a  sheet  of  wax  or  other  plastic  material,  thus  making  a  mould. 
The  interior  of  this  mould  is  then  dusted  with  very  finely  powdered 
graphite  or  bronze  by  which  the  surface  is  made  a  conductor,  and 
using  this  as  the  cathode  a  thin  layer  of  copper  is  deposited  upon 
it.  This  thin  layer  is  then  backed  by  pouring  into  it  melted  type 
metal  and  the  resulting  plate  is  fastened  to  a  wooden  block. 


182  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  22. 
THE   STORAGE   BATTERY. 

236.  Reversibility  of  Cells. — Should  a  simple  zinc-carbon  cell 
be  connected  in  closed  circuit,  a  current  will  be  produced  and 
while  it  is  flowing  the  zinc  will  waste  away  and  go  into  solution 
as  zinc  sulphate,  the  electrolyte  will  grow  weaker  and  hydrogen 
will  be  evolved  at  the  carbon  plate.     Suppose  now  the  circuit  to 
be  broken  and  that  there  be  inserted  in  it  a  battery  or  an  electrical 
machine  faced  in  the  opposite  direction  to  the  original  cell.    If 
this  battery  or  machine  produces  a  greater  electro-motive  force 
than  the  ceH,  a  current  will  be  set  up  opposite  to  the  original  cur- 
rent and  will  flow  through  the  cell  in  a  reverse  direction,  that  is, 
the  simple  cell  now  becomes  an  electrolytic  cell  (Par.  220).    The 
zinc  sulphate  in  solution  will  be  decomposed,  the  zinc  being  rede- 
posited  upon  the  zinc  plate  (Par.  224),  the  electrolyte  increasing 
in  strength  and  oxygen  being  released  at  the  carbon  plate,  in  other 
words,  if  the  current  continues  to  flow  for  a  sufficient  length  of 
time  the  previous  chemical  action  will  be  undone  and,  with  the 
exception  of  the  loss  of  a  small  amount  of  water  in  the  form  of 
hydrogen  and  oxygen,  the  cell  will  be  restored  to  its  primary  con- 
dition.   Such  a  cell  is  said  to  be  reversible.    It  is  evident  that  a 
primary  cell  in  which  the  chemical  action  results  in  the  escape  in 
the  form  of  gas  of  a  portion  of  the  active  material  can  not  be  en- 
tirely reversible. 

237.  Storage  Battery. — A  cell   which  is  thus  reversible  and 
which  when  exhausted  is  regenerated  by  passing  through  it  from 
an  extraneous  source  of  electrical  energy  a  current  opposite  in 
direction  to  the  flow  of  discharge,  is  called  a  secondary  cell,  or  an 
accumulator,   or,    more   commonly,    a   storage   battery,   although 
strictly  the  word  "battery,"  as  already  pointed  out,  should  be 
applied  to  a  group  of  two  or  more  cells.    When  such  a  battery 
approaches  exhaustion  it  is  said  to  be  discharged,  and  the  operation 
of  restoring  it  is  called  charging.    As  commonly  understood,  a 
storage  battery  is  one  whose  primary  condition  is  that  of  exhaus- 


VOLTAIC  ELECTRICITY.  183 

tion,  that  is,  one  which  can  not  be  used  until  it  has  first  been 
charged.  Reflection  will  show  that  the  charging  current  must 
enter  the  battery  by  the  same  pole  from  which  the  discharging 
current  leaves,  that  is,  by  the  positive  pole.  The  academic  dis- 
tinction between  the  positive  pole  and  the  positive  plate  of  voltaic 
cells  (Par.  193)  is  not  observed  in  dealing  with  storage  batteries 
and  the  positive  plate  is  that  which  carries  the  positive  pole  and  is 
that  plate  from  which  the  current  issues  on  discharge  and  by  which 
it  enters  on  charge.  In  these  storage  batteries  there  is  no  elec- 
tricity stored  up.  The  charging  current  enters  at  the  positive 
pole,  passes  through  the  battery  and  leaves  by  the  negative  pole, 
but  in  its  passage  it  performs  chemical  work  or  builds  up  a  certain 
chemical  potential  which  later  produces  electrical  energy  when  the 
proper  connections  are  made. 

238.  Elements  of  a  Secondary  Cell. — Experiments  have  been 
conducted  with  many  substances  to  determine  their  fitness  for 
the  elements  of  a  secondary  cell  but,  with  the  exception  of 
the  recently  introduced  nickel-iron-potassium  hydroxide  cell  of 
Edison  (Par.  250),  the  great  majority  of  storage  batteries  employ 
positive  plates  of  lead  peroxide,  Pb02,  negative  plates  of  pure 
lead,  and  an  electrolyte  of  dilute  sulphuric  acid  of  a  specific 
gravity  of  about  1.20,  or  about  one  part  of  acid  by  bulk  to  five  of 
water.    There  are  many  objections  to  lead;  it  is  very  heavy,  it  is 
soft,  and  the  workmen  in  it  frequently  suffer  from  lead  poisoning. 
There  must  then  be  some  peculiar  qualities  of  lead  which  outweigh 
these  disadvantages.    Upon  examining  its  chemical  properties  we 
are  at  once  struck  by  the  fact  that  it  is  the  only  commercial  metal 
whose  sulphate  is  insoluble.     When,  therefore,  the  electrolyte 
attacks  the  plates  and  produces  lead  sulphate,  this  salt  does  not 
pass  off  into  solution  but  remains  at  the  precise  spot  where  formed 
and  when  the  cell  is  charged  the  sulphate  is  reconverted  into  lead 
without  any  change  of  position.     Repeated  charging  and  dis- 
charging, therefore,  does  not  materially  alter  the  shape  of  the 
plates. 

239.  Preparation  of  the  Plates. — The  peroxide  of  lead  of  the 
positive  plate  and  the  pure  lead  of  the  negative  plate  are  designated 
as  the  active  material  of  the  cell.    Since  the  chemical  action,  the 
source  of  the  electrical  energy  developed,  takes  place  only  at 
the  surface  of  contact  of  the  active  material  and  the  electrolyte, 


184  ELEMENTS  OF  ELECTRICITY. 

the  object  held  in  view  in  preparing  the  plates  is  to  give  to  this 
active  material  the  maximum  amount  of  surface.  This  object  is 
attained  in  any  one  or  combination  of  three  ways. 

(a)  Mechanical. — The  plate  may  be  deeply  incised,  or  grooved, 
or  fluted,  or  thin  tape-like  ribbons  of  lead  may  be  corrugated, 
coiled  up  and  inserted  in  apertures  in  the  plate  proper,  or  the  active 
material  may  be  applied  to  the  plate  as  a  paste,  or  it  may  be 
powdered  and  placed  in  perforated  receptacles  which  are  attached 
to  the  plate. 

(b)  Chemical. — The  metal  may  be  eaten  by  acids  until  it 
becomes  more  or  less  spongy,  or  it  may  be  cast  mixed  with  a 
granulated  substance  which  is  subsequently  dissolved  out  leaving 
the  plate  porous. 

(c)  Electrolytic. — The  plate  may  have  attached  to  it  or  enclosed 
in  cavities  in  it  a  salt  of  the  metal,  which  salt,  as  may  be  desired, 
is  either  converted  by  electrolytic  action  into  the  peroxide  or  else 
reduced  to  a  finely  divided  metallic  state. 

Since  neither  the  peroxide  nor  the  spongy  lead  possess  the 
requisite  mechanical  strength  for  plates,  the  active  material  is 
generally  contained  or  supported  in  spaces  between  the  ribs  of  a 
grid-iron  shaped  frame  of  lead.  On  this  account,  the  plates  are 
frequently  called  grids. 

240.  The  Plante  Cell. — The  first  storage  batteries  were  pro- 
duced by  Plante  in  1860.  The  plates  were  prepared  by  placing 
face  to  face,  and  separated  by  a  layer  of  felt  two  thin  sheets  of  lead 
which  were  rolled  up  spirally  into  a  cylinder  and  placed  in  a  cell 
containing  dilute  sulphuric  acid.  On  passing  a  current  through 
the  cell  the  water  was  decomposed  (Par.  219)  and  the  oxygen 
released  at  the  anode  converted  the  surface  of  this  plate  into  the 
peroxide.  After  a  number  of  hours  the  current  was  reversed. 
The  other  plate  now  became  the  anode  and  was  converted  into  the 
peroxide,  while  the  hydrogen  released  at  the  cathode  reduced  the 
former  peroxide  to  metallic  lead,  leaving  it  in  a  spongy  condition. 
The  current  was  thus  reversed  several  times  and  each  time  the 
chemical  action  penetrated  more  deeply  into  the  plates,  or  the 
plates  were  said  to  be  "worked  up."  It  will  be  seen  in  the  follow- 
ing paragraphs  that  the  principle  of  the  preparation  of  the  plates 
in  more  modern  storage  batteries  is  the  same,  although  the  details 
are  different. 


VOLTAIC  ELECTRICITY. 


185 


241.  The  Chloride  Accumulator. — A  well  known  form  of 
storage  battery  is  the  chloride  accumulator ,  so  called  because  in 
the  manufacture  of  the  earlier  forms  the  chlorides  of  zinc  and  lead 
were  used.  In  preparing  the  negative  plates,  the  powdered 
chlorides  of  lead  and  zinc  were  intimately  mixed  and  melted  and 
the  fused  mass  was  then  cast  into  little  blocks  a  quarter  of  an  inch 
thick  and  about  an  inch  square.  These  blocks  were  then  placed 
in  a  mould,  arranged  in  regular  order  and  evenly  spaced,  and 
melted  lead  was  poured  into  the  mould.  The  resulting  plate  can 
be  compared  to  a  window  sash,  the  lead  corresponding  to  the  wood 


ii 


Fig.  109. 


work  and  the  chloride  blocks  to  the  panes  (Fig.  109  a).  The  plate 
was  next  soaked  in  water  which  dissolved  out  and  removed  the 
zinc  chloride  and  left  the  lead  chloride  in  a  porous  condition. 
Finally,  this  plate  was  made  the  cathode  of  an  electrolytic  cell 
and  a  current  passed  through  it  until  the  lead  chloride  was  entirely 
reduced  to  spongy  lead.  In  more  recent  forms  the  negative  grid 
is  composed  of  two  faces  each  containing  shallow  rectangular 
cavities,  the  bottoms  of  these  being  finely  perforated.  They  are 
filled  with  one  of  the  oxides  of  lead,  the  two  faces  are  then  pressed 


186  ELEMENTS  OF  ELECTRICITY. 

together  and  rivetted  firmly.  The  perforations  permit  the 
electrolyte  to  reach  the  lead  oxide  which  by  electrolytic  action  is 
reduced  to  spongy  lead. 

The  grid  for  the  positive  plate  was  made  of  lead  which,  for  the 
sake  of  hardness,  was  alloyed  with  a  small  amount  of  antimony. 
It  was  cast  with  rows  of  circular  openings  (Fig.  109  6)  which  were 
not  cylindrical  but  contracted  towards  the  center  of  the  plate. 
Thin  corrugated  ribbons  of  lead  were  rolled  up  into  cylinders  and 
pressed  into  these  openings,  the  shape  of  the  openings  causing  the 
cylinders  to  be  held  firmly.  The  plate  was  then  made  the  anode 
of  an  electrolytic  cell  for  about  30  hours,  the  oxygen  released  by 
the  current  converting  a  part  of  the  lead  into  lead  peroxide.  The 
amount  of  active  material  is  sometimes  increased  by  filling  the 
crevices  in  the  corrugated  tape  with  a  paste  of  either  red  lead, 
Pb304,  or  of  litharge,  PbO,  both  of  which  become  peroxide  in  the 
electrolytic  cell. 

242.  Shape  and  Size  of  Plates. — The  plates,  except  the  largest 
sizes,  are  square.     The  thickness  of  the  smaller  plates  is  one- 
quarter  of  an  inch  but  for  the  sake  of  strength  this  is  increased  to 
one-half  inch  in  the  larger  ones.    The  size  varies  with  the  current 
which  the  battery  is  designed  to  furnish  when  discharged  at  its 
normal  rate,  that  is,  at  the  rate  which  experience  has  shown  can 
not  be  exceeded  without  more  or  less  injury  to  the  plate.    This  is 
generally  taken  as  about  six  amperes  per  square  foot  of  positive 
plate  surface.     Thus  the  E  plate  of  the  chloride  accumulator 
measures  7.75x7.75  inches,  or  120  square  inches,  which  is  five- 
sixths  of  a  square  foot,  and  the  normal  rate  is  given  by  its  manu- 
facturers as  five  amperes.    If  the  cell  contains  three  of  these  plates, 
its  normal  rate  is  15  amperes,  etc.    The  plates  of  this  battery  are 
designated  by  the  letters  of  the  alphabet,  the  B  plate  being  the 
smallest  and  measuring  3x3  inches,  and  each  has  twice  the  active 
surface  and  twice  the  normal  rate  of  the  next  smaller  size.    Thus 
the  normal  rate  of  an  F  plate  is  ten  amperes. 

243.  Grouping  of  Plates. — The  plates  are  cast  with  three  lugs 
at  the  top.    Two  of  these  rest  on  the  opposite  sides  of  the  cell 
when  the  plate  is  in  position,  support  its  weight  and  keep  it  an 
inch  or  so  above  the  bottom  of  the  cell  (Fig.  110).    The  third  is 
used  to  join  the  similar  plates  of  one  cell  to  a  common  terminal  or 
cross  strap.    They  fit  into  holes  mortised  in  the  cross  strap  and 


VOLTAIC  ELECTRICITY. 


187 


are  "burned"  to  the  strap  by  a  hydrogen  flame,  the  hydrogen 
reducing  any  oxide  on  the  surface  of  the  molten  metal  and  thus 
allowing  a  perfect  joint  to  be  formed. 

The  number  of  plates  is  always  odd,  there  being  one  more 
negative  plate,  so  that  each  positive  plate  has  a  negative  plate 
presented  to  each  of  its  faces.  The  smallest  number  of  plates  is 
therefore  three;  on  the  other  hand,  cells  are  made  which  contain 
75  or  more.  The  total  number  of  plates  per  cell  is  indicated  by  a 
subscript  after  the  letter  designating  the  size,  as  B%,  C5,  etc. 


HI 


Fig.  110. 

The  cells,  except  those  of  large  size  and  those  for  use  in  vehicles, 
are  of  glass.  They  frequently  rest  in  shallow  boxes  which  contain 
sand  so  as  to  distribute  the  weight  evenly  over  the  bottom,  the 
boxes  in  turn  resting  on  insulating  glass  supports.  The  cells  for 
vehicles  are  of  hard  rubber  and  have  rubber  covers.  The  larger 
cells  are  lead-lined  wooden  tanks.  The  largest  chloride  accumu- 
lator cell  contains  75  plates,  each  15x31  inches,  weighs  three  tons 
and  will  furnish  1500  amperes  for  eight  hours. 


188 


ELEMENTS  OF  ELECTRICITY. 


Should  dissimilar  plates  touch  each  other  directly  or  be  put  in 
contact  through  any  sediment  at  the  bottom  of  the  cell,  they  will 
be  short  circuited  (Par.  306).  For  this  reason  they  are  held  apart 
by  some  form  of  fender  or  "separator,"  and,  as  stated  above,  are 
supported  an  inch  or  so  above  the  bottom  of  the  cell.  Formerly 
rods  of  glass  or  of  hard  rubber  were  used  as  separators  but  now 
preference  is  given  to  thin  wooden  boards  of  the  thickness  used  in 
making  berry  boxes.  Owing  to  this  compact  arrangement  of  the 
plates  the  internal  resistance  of  a  storage  cell  is  very  small  (Par. 
294),  usually  something  less  than  one-thousandth  of  an  ohm. 

244.  Reaction  on  Discharge  and  Charge. — When  the  cell  has 
been  completely  charged,  the  active  material  of  the  positive  plate 
being  lead  peroxide  and  that  of  the  negative  plate  spongy  lead, 
we  have  the  requisite  conditions  for  a  simple  voltaic  cell  (Par.  201), 
that  is,  two  conducting  substances  immersed  in  a  liquid  which 
attacks  one  more  freely  than  it  does  the  other.  When  the  circuit 
is  closed  the  electrolyte  attacks  the  negative  plate  (Fig.  Ill  a) 


Fig.  111. 

producing  lead  sulphate.  Hydrogen  released  at  the  positive  plate 
is  converted  into  water  at  the  expense  of  the  oxygen  of  the  per- 
oxide, that  is,  the  peroxide  is  the  depolarizer  of  the  cell.  When  the 
peroxide  has  thus  been  deoxidized,  the  remaining  lead  is  attacked 
by  the  electrolyte,  producing  lead  sulphate  and  action  ceases.  In 
practice  however,  the  cell  is  recharged  before  this  limit  is  reached. 
The  reaction  may  be  written 


Positive 
Plate 


Electro- 
lyte 


Negative 
Plate 


Positive 
Plate 


Electro- 
lyte 


Negative 
Plate 


Pb02+  2H2S04+       Pb     =  PbS04 
although  actually  it  is  more  complicated. 


2H20     +PbS0 


VOLTAIC  ELECTRICITY.  189 

It  will  be  noted  that  during  discharge  the  acid  is  withdrawn 
from  the  electrolyte  and  goes  into  combination  with  the  plates 
and  that  water  is  released  in  its  stead,  that  is,  the  E.  M.  F.  of  the 
cell  decreases,  the  resistance  of  the  electrolyte  increases  and  its 
specific  gravity  decreases. 

The  reactions  on  charge  are  the  reverse  of  those  on  discharge. 
Fig.  Ill  b  represents  diagrammatically  an  electric  generator  send- 
ing a  current  through  the  cell,  both  jpf  whose  plates  are  supposed 
to  have  become  lead  sulphate.  The  water  of  the  electrolyte  is 
decomposed,  the  hydrogen  removing  the  S04  from  the  plates  and 
forming  again  H2S04,  and  the  oxygen  released  at  the  positive  plate 
reconverting  the  lead  into  the  peroxide.  The  reaction  is 

Positive  Electro-  Negative  Positive  Electro-  Negative 

Plate  lyte  Plate  Plate  lyte  Plate 

PbS04  +  2H20  +  PbS04  =  Pb02  +  2H2S04  +    Pb 
As  a  result  of  this,  the  E.  M.  F.  of  the  cell  rises,  the  resistance 
of  the  electrolyte  decreases  and  its  specific  gravity  increases. 

245.  Charging. — The  current  for  charging  a  storage  battery  is 
generally  furnished  by  a  generator,  though  a  battery  of  a  few  cells 
may  be  charged  from  a  larger  battery.    This  current,  as  has  al- 
ready been  stated,  is  brought  in  at  the  positive  pole  of  the  battery. 
Its  E.  M.  F.  should  be  from  5  to  10  per  cent  greater  than  that  of 
the  battery  and  since  the  E.  M.  F.  of  the  battery  rises  as  the 
charging  progresses,  there  must  be  some  arrangement  by  which 
the  charging  E.  M.  F.  may  be  increased  correspondingly.    If  the 
E.  M.  F.  of  the  source  of  supply  be  less  than  that  of  the  battery, 
the  latter  during  charging  must  be  subdivided  into  groups  which 
are  conveniently  charged  in  parallel  (Par.  336).    When  a  battery 
is  discharged  it  must  be  recharged  at  once,  for  if  the  discharged 
plates  remain  in  the  acid  for  even  a  short  time  they  become  in- 
jured (Par.  247).    The  rate  at  which  the  battery  is  charged  is  fixed 
by  the  makers  and  averages  about  ten  per  cent  less  than  the  normal 
rate  of  discharge.    It  can  not  be  exceeded  without  risk.    At  least 
as  much  time  is  required  to  charge  a  battery  as  to  discharge  it. 
When  a  battery  is  put  into  commission  for  the  first  time  it  has  to 
be  charged  at  the  normal  rate  for  from  45  to  55  hours  continuously 
but  thereafter  the  normal  time  is  about  eight  or  nine  hours. 

246.  Indications  of  Charge. — It  is  important  to  be  able  to  tell 
when  a  battery  is  properly  charged.     The  indications  usually 
relied  upon  are  the  following: — 


190 


ELEMENTS  OF  ELECTRICITY. 


(a)  Voltage.—  A  new  cell,  when  fully  charged  and  while  still 
receiving  the  charging  current,  should  have  a  voltage  of  2.5  or  even 
slightly  more,  but  this  decreases  with  age.  When  current  is 
drawn  from  the  cell  the  voltage  almost  immediately  falls  to  2.05 
or  2.0  after  which  it  decreases  slowly  and  steadily  until  the  cell 
approaches  exhaustion  at  which  point  it  begins  to  drop  rapidly 
(Fig.  112).  A  cell  should  never  be  discharged  to  a  lower  voltage 
than  1.7  and  if  it  reaches  this  point  should  be  recharged  at  once. 
In  actual  charging  the  process  is  continued  until  three  successive 
readings  of  the  voltmeter  at  intervals  of  fifteen  minutes  show  no 
further  rise.  Usually  some  average  interior  cell  of  the  battery  is 


VOLTS 
3.0 


2.4 
Jt.fc 


1.6 


CHARGE 


Fig.  112. 

selected  as  a  "pilot  cell"  and  its  voltage  is  taken  as  an  indication 
of  that  of  the  others.  In  order  that  these  observations  may  be 
of  any  value,  the  voltage  must  be  taken  while  the  battery  is  either 
being  charged  or  discharged  at  the  normal  rate. 

(b)  Specific  gravity  of  the  electrolyte. — Examination  of  the 
reactions  given  in  Par.  244  shows  that  during  charge  sulphuric 
acid  is  driven  out  from  its  combination  with  the  plates  and  is 
released  in  the  electrolyte.  The  specific  gravity  of  sulphuric  acid 
(1.834)  being  nearly  twice  as  great  as  that  of  water,  that  of 
the  electrolyte  rises  accordingly.  When  discharged,  the  specific 
gravity  of  the  electrolyte  may  fall  as  low  as  1.175  or  even  less, 
and  when  charged  it  should  lie  between  1.200  and  1.210.  The 
specific  gravity  is  read  from  a  hydrometer,  a  little  lead-weighted, 
flattened  glass  float  having  a  slender  graduated  stem  and  look- 


VOLTAIC  ELECTRICITY.  191 

ing  somewhat  like  a  thermometer  (Fig.  113).  As  the  density 
of  the  electrolyte  decreases  the  hydrometer  sinks  deeper  into 
the  liquid;  as  it  increases,  the  hydrometer  floats  higher 
and  in  each  case  the  corresponding  specific  gravity  is 
indicated  by  the  graduation  on  the  stem  of  the  instrument 
reached  by  the  surface  of  the  electrolyte. 

(c)  Gassing. — When  bubbles  of  gas  begin  to  rise  freely 
in  the  cell,  giving  the  liquid  the  appearance  of  boiling,  the 
current  has  completed  its  work  upon  the  plates  and  is 
decomposing  the  electrolyte,  the  charging  therefore  should 
not  be  pushed-  farther.    These  mixed  gases  are  explosive, 
therefore  the  storage  battery  room  should  be  well  venti- 
lated and  no  flame  should  be  taken  into  the  room  when 
the  cells  are  gassing. 

(d)  Color  of  the  plates. — When  fully  charged  the  positive 
plates  are  of  a  rich  chocolate  color,  the  negative  plates  a 
lead  grey,  and  these  colors  afford  the  expert  a  means  of 
judging  of  the  state  of  charge. 

247.  Troubles  of  Lead  Batteries. — If  a  lead-sulphuric 
acid  battery  be  charged  or  discharged  at  an  excessive 
rate,  or  be  allowed  to  stand  discharged,  the  acid  attacks 
the  plates  and  forms  a  white  coating  supposed  to  be  the 

basic  lead-sulphate  Pb2S05.  The  plates  are  then  said  to  be 
sulphated.  This  coating  is  insoluble  and  a  non-conductor  and 
practically  removes  from  action  the  part  of  the  plate  which  it 
effects.  When  not  too  extensive,  it  may  sometimes  be  removed 
by  repeated  charging  and  discharging  of  the  cells. 

The  crystals  of  sulphate  forming  within  the  porous  portions  of 
the  plate  sometimes  act  as  wedges  and  cause  the  plate  to  buckle, 
that  is,  to  bulge  out  in  a  dish  shape.  This  usually  loosens  and 
causes  a  loss  of  the  active  material  of  the  plate  and  may  produce 
a  short  circuit  with  the  adjacent  plates  of  the  cell. 

248.  Care  of  Lead  Batteries. — Lead  batteries  must  be  given 
constant  attention.    Charging  should  be  done  at  regular  intervals 
and  the  battery  must  never  be  allowed  to  stand  discharged.    Each 
cell  should  be  numbered;  these  numbers  should  be  entered  in  a 
blank  book  and  a  weekly  record  should  be  kept  of  the  voltage  and 
the  specific  gravity  of  each  cell.     Inspection  of  this  record  will 
frequently  reveal  incipient  trouble  in  individual  cells  and  will  thus 


192  ELEMENTS  OF  ELECTRICITY. 

enable  corrections  to  be  applied  before  serious  damage  has  occurred. 
A  battery  should  not  long  remain  idle.  If  it  is  not  to  be  used 
for  some  months  it  should  be  put  out  of  commission.  It  is  charged 
fully,  thus  expelling  into  the  electrolyte  the  acid  in  combination 
with  the  plates.  The  electrolyte  is  then  syphoned  off  into  carboys, 
the  cells  filled  with  water  and  allowed  to  stand  for  48  hours,  after 
which  the  water  is  drawn  off. 

249.  Objections  to  Lead  Batteries. — The  principal  objections 
advanced  against  lead  batteries  are— 

(a)  Poisonous  effect  of  lead  upon  the  workmen  engaged  in  the 
manufacture  of  the  plates. 

(b)  Excessive  weight  of  the  plates,  lead  being  the  heaviest  of 
the  commercial  metals. 

(c)  Fragility  of  the  cells  and  inability  to  stand  shocks  and  jars. 

(d)  Need  of  constant  supervision  by  an  expert  electrician  for 
proper  care  of  the  battery. 

(e)  Injury  resulting  to  the  battery  if  it  remains  uncharged  for 
any  length  of  time. 

(f)  Injury  resulting  to  the  battery  if  it  remains  long  charged 
and  hence  necessity  of  charging  and  discharging  even  when  use 
of  battery  is  not  required. 

(g)  Injury  produced  by  short  circuits  or  by  charging  or  dis- 
charging at  excessive  rates. 

(h)  Injury  produced  by  using  the  battery  if  the  temperature 
rises  above  100°  F. 

(i)  Loss  of  active  material  from  the  plates. 

(j)  Production  of  acid  vapors  highly  irritating  to  the  throat 
and  lungs  and  corrosive  to  surrounding  objects  of  metal. 

(k)  Production  of  explosive  gases. 

(1)  Loss  of  charge  on  standing.  This  amounts  to  about  25  per 
cent  per  week. 

The  foregoing  indicates  that  the  lead  battery  is  most  advan- 
tageously employed  when  it  is  installed  in  a  suitable  build- 
ing and  subjected  to  constant  use  under  the  supervision  of  a 
trained  electrician,  and  that  it  is  not  well  adapted  for  service  in 
vehicles  used  roughly  and  irregularly  and  cared  for  by  unskilled 
attendants. 


VOLTAIC  ELECTRICITY 


193 


250.  The  Edison  Storage  Battery. — The  Edison  storage  battery 
is  designed  primarily  for  use  in  vehicles  and  has  been  developed 
to  avoid  as  far  as  possible  the  objections  enumerated  in  the  pre- 
ceding paragraph.  In  this  battery  the  active  material  of  the 
positive  plate  is  nickel  peroxide,  Ni203,  that  of  the  negative  plate 
is  finely  divided  iron,  and  the  electrolyte  is  a  21  per  cent  solution 
of  potassium  hydroxide,  KOH,  to  which  is  added  a  small  amount 
of  lithium  hydroxide.  The  grids  are  of  nickel-plated  steel. 

The  active  material  of  the  positive  plate,  initially  in  the  form  of 
nickel  hydroxide,  Ni(OH)2,  is  packed  in  small  pencil-like  perforated 
tubes  of  nickel-plated  steel  which  are  securely  fastened  to  the  grid 
(Fig.  114  a) .  To  improve  the  conductivity  of  this  active  material, 


Fig.  114. 

it  is  interspersed  with  layers  of  extremely  thin  nickel  flakes,  there 
being  as  many  as  350  layers  in  each  tube  in  a  length  of  about  four 
inches.  These  tubes  are  banded  at  intervals  by  steel  hoops  which 
prevent  any  expansion  due  to  swelling  of  the  material  within.  The 
active  material  of  the  negative  plate,  primarily  ferrous  oxide, 
FeO,  is  packed  into  flat  perforated  pockets  of  nickeled  steel  which 
are  forced  into  the  grid  under  pressure.  A  small  per  cent  of  mer- 
cury is  added  to  the  oxide  to  improve  its  conductivity. 


194  ELEMENTS  OF  ELECTRICITY. 

The  plates  are  held  together  by  nickeled-steel  cross  bolts  which 
also  carry  the  terminals.  Opposite  plates  are  held  apart  by  rubber 
separators.  The  cells  are  of  nickel-plated  sheet  steel,  corrugated 
for  rigidity  (Fig.  114  6).  The  assembled  plates,  protected  on  all 
sides  by  rubber  fenders,  are  fitted  tightly  into  the  cell  which  is 
then  closed  by  a  steel  lid  which  is  welded  on.  This  lid  contains 
an  opening  through  which  electrolyte  may  be  introduced  and  is 
arranged  with  a  valve  which  permits  gas  to  escape  from  the  cell 
but  prevents  gas  from  entering.  Potassium  hydroxide  has  a  great 
affinity  for  carbonic  acid  gas,  C02,  which,  if  the  cell  were  left  open, 
would  rapidly  injure  the  electrolyte. 

There  are  two  regular  sizes  of  plates  designated  A  and  B.  The 
A  plates  are  the  larger,  the  rectangular  portion  being  about 
5x12  inches.  A  number  following  the  letter,  as  A-4,  indicates 
not  the  total  number  of  plates  but  the  number  of  positive  plates 
in  the  cell.  The  normal  rate  of  discharge  of  an  A  plate  is  seven 
and  a  half  amperes.  The  normal  rate  of  an  A-4  cell  is  therefore 
thirty  amperes. 

251.  Reactions  of  the  Edison  Battery.—  In  Par.  223  it  was 
shown  that  when  a  current  is  passed  through  a  solution  of  KOH 
the  effect  is  merely  to  electrolyze  the  water.  On  the  first  charge 
the  oxygen  released  at  the  anode  converts  the  nickel  hydroxide 
into  the  peroxide,  thus— 

2Ni(OH)2  +0  =  Ni203  +2H20 

and  the   hydrogen 
released  at  the  cathode  reduces  the  iron  oxide  to  metallic  iron 


On  discharge  the  reaction  is  as  follows: 

Positive  Electro-  Negative         Positive  Electro-  Negative 

Plate  lyte  Plate  Plate  lyte  Plate 


On  charge  this  is  reversed,  or 

Positive               Electro-             Negative          Positive                    Electro-  Negative 

Plate                     lyte                    Plate                Plate                           lyte  Plate 

+  Fe 


From  the  preceding  it  is  seen  that  the  reactions  in  the  cell  con- 
sist in  the  transfer  of  oxygen  back  and  forth  and  that  the  electro- 
lyte is  unaltered.  It  may  therefore  be  reduced  to  a  minimum  with 


VOLTAIC  ELECTRICITY. 


195 


a  corresponding  saving  of  bulk  and  weight.  It  would  also  seem 
that  it  should  last  indefinitely  but,  as  stated  in  the  preceding 
paragraph,  it  absorbs  and  combines  readily  with  carbon  dioxide 
and  on  this  account  should  be  renewed  yearly. 

252.  Charging  the  Edison  Battery.— Since  the  electrolyte 
remains  unaltered  during  charge  and  discharge  and  since  the 
plates  are  enclosed  in  an  hermetically  sealed  steel  case,  the  only 
indication  of  charge  of  an  Edison  cell  is  its  voltage  taken  while 
charging  or  discharging.  During  charge  the  voltage  gradually 
rises  (Fig.  115)  until  when  fully  charged  and  receiving  current  it 

VOUTS 


2.0 
1.8 
3.6 
1.4 

j.a 
J.o 


CHARgE 


^  >-  HOURS 


Fig.  115. 

reaches  a  maximum  of  1.84.  When  current  is  drawn  from  the  cell 
the  voltage  drops  at  once  to  about  1.4  and  then  falls  gradually, 
averaging  about  1.2  volts  until  near  the  end  when  it  drops  rapidly 
to  one  volt.  On  the  average,  a  battery  is  charged  at  the  normal 
rate  in  seven  hours  and  discharges  in  about  six. 

253.  Advantages  and  Disadvantages  of  the  Edison  Battery. — 

The  advantages  of  the  Edison  battery  are  in  marked  contrast  to 
the  disadvantages  of  the  lead  battery  as  enumerated  in  Par.  249. 
Thus— 

(a)  Although  the  salts  of  nickel  are  poisonous,  the  workmen 
preparing  the  plates  are  free  from  danger. 

(b)  The  plates  are  lighter  than  corresponding  lead  plates. 

(c)  The  cells  could  hardly  be  improved  as  regards  strength. 
They  are  uninjured  by  the  most  violent  jolts  and  jars  to  which  a 
vehicle  may  be  exposed. 

(d)  They  require  a  minimum  of  attention. 

(e)  They  may  be  left  without  injury  at  any  state  of  charge  or 
discharge. 


196  ELEMENTS  OF  ELECTRICITY. 

(f )  They  may  be  charged  or  discharged  at  excessive  rates,  may 
be  overcharged,  short  circuited,  or  even  reversed  without  per- 
manent injury. 

(g)  They  produce  no  irritating  or  corrosive  fumes,  in  fact,  by 
the  absorption  of  carbon  dioxide  they  purify  the  air.    This  last 
renders  them  especially  valuable  in  submarines. 

The  disadvantages  of  the  Edison  cell  are — 

(a)  Low  voltage;  only  1.2  as  compared  to  nearly  2.0  of  the  lead 
cell,  hence  a  greater  number  of  cells  required. 

(b)  Decrease  of  activity  at  temperatures  below  40°  F. 
<c)  Greater  cost  than  lead  cell. 

The  efficiency  (ratio  of  energy  delivered  by  the  cell  to  that 
'spent  in  charging  it)  of  the  lead  cell  is  about  75  per  cent;  that  of 
the  Edison  cell  is  only  60  per  cent,  but  weight  for  weight  the 
efficiency  of  the  Edison  cell  is  the  greater. 

254.  Use  of  Storage  Batteries. — It  requires  more  time  to  charge 
a  storage  battery  than  it  does  to  discharge  it.  We  have  just  seen 
that  the  efficiency  does  not  exceed  75  per  cent.  There  is  therefore 
a  loss  of  both  time  and  energy  and  the  question  arises  why  should 
storage  batteries  be  employed.  This  is  best  answered  by  an 
enumeration  of  some  of  the  commoner  uses  of  storage  batteries. 
These  are— 

(a)  As  a  portable  source  of  power  and  light  for  vehicles,  launches 
and  submarine  boats;  also  for  furnishing  the  ignition  spark  for 
automobiles. 

(b)  As  a  source  of  power  and  light  in  public  buildings,  hotels, 
etc.,  to  run  lights,  elevators,  etc.,  after  the  engines  have  been  shut 
down  for  the  night  and  thus  to  save  the  expense  of  an  extra  shift 
of  engineers  and  firemen. 

(c)  As  a  reserve  in  electrical  power  plants,  supplying  power 
during  a  temporary  stopping  of  the  engines  for  adjustment,  over- 
hauling or  repairs. 

(d)  To  light  the  magazines  of  a  fortification  and  to  operate  the 
mine  and  the  range  finding  systems. 

(e)  To  carry  the  "peak  loads"  of  an  electric  railroad  or  of  a 
lighting  plant.    Such  a  plant  must  be  able  to  supply  the  maximum 
current  required  during  the  rush  hours.    It  is  also  operated  most 
efficiently  when  the  engines  are  run  at  a  uniform  rate.    If  it  sup- 
plied constantly  the  maximum  current  there  would  be  much 


VOLTAIC  ELECTRICITY. 


197 


waste  during  the  slack  hours.  The  curve  in  Fig.  116  may  be  taken 
to  represent  the  operation  of  a  trolley  line  during  24  hours,  the 
horizontal  axis  being  the  axis  of  time,  the  vertical  heights  repre- 
senting the  power  supplied  by  the  electric  plant  and  consequently 


iZP-M. 


4  A.M. 


SAM. 


fitM 

Fig.  116 


JfcP.K 


the  area  of  the  curve  representing  work  performed.  If  the  line 
AB  represents  the  constant  output  of  the  engines,  the  shaded 
areas  represent  surplus  energy  which  may  be  applied  to  charging 
a  storage  battery,  the  battery  in  turn  being  called  upon  to  give 
back  energy  when  the  peak  loads  occur  at  8  A.  M.  and  at  6  P.  M. 
There  are  other  uses  of  the  storage  battery  but  they  can  not 
be  explained  until  our  subject  has  been  further  developed. 


198  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  23. 

THEORY   OF   ELECTROLYTIC   DISSOCIATION. 

255.  Interdependence  of  the  Physical  Sciences. — The  more 
our  knowledge  of  the  physical  sciences  is  increased,  the  more  we 
realize  their  interrelation  and  their  interdependence.  The  study 
of  no  particular  one  can  be  successfully  pursued  if  we  exclude  the 
help  afforded  and  the  side  lights  thrown  upon  it  by  others.  This 
is  notably  so  in  the  case  of  electricity.  For  a  proper  understanding 
of  the  present  accepted  theory  accounting  for  the  phenomena  of 
voltaic  electricity,  we  must  turn  to  physical  chemistry  and  to 
develop  our  explanation  must  begin  with  certain  facts  which  at 
first  sight  appear  to  have  not  even  a  remote  connection  with  our 
announced  subject. 

The  following  outline  will  assist  the  student  in  following  the 
thread  of  connection  between  the  facts  which  will  now  be  brought 
out: 

1.  Avogadro's  law  and  a  derived  corollary  applicable  to  gase- 
ous pressure  are  explained  (Par.  256). 

2.  Exceptions  to  the  law  of  gaseous  pressure  are  shown  to  be 
due  to  dissociation  which  is  defined  (Pars.  257-258). 

3.  Osmotic  pressure  is  described  and  its  observation  and  meas- 
urement explained  (Pars.  259-262). 

4.  Osmotic  pressure  is  shown  to  follow  the  laws  of  gaseous 
pressure  (Pars.  263-266). 

5.  Abnormal    osmotic   pressures   are,    like   excessive   gaseous 
pressures,  shown  to  be  capable  of  explanation  under  the  supposi- 
tion of  dissociation,  otherwise  called  ionization  (Pars.  267-268). 

6.  Ionization  is  further  explained  (Pars.  269-274) . 

7.  Electrolytic  properties  are  shown  to  depend  upon  ionization 
(Pars.  275-279). 

8.  Electricity  is  shown  to  be  atomic  in  character  (Par.  280). 

256.  Laws  of  Variation  of  Gaseous  Pressure. — Avogadro's 
Law,  of  fundamental  importance  in  Chemistry,  is  to  the  effect 
that  under  like  conditions  of  temperature  and  pressure,  equal 


VOLTAIC  ELECTRICITY.  199 

volumes  of  all  gases,  simple  or  compound,  contain  the  same  num- 
ber of  molecules.  If  we  should  have  a  series  of  cylinders  of  exactly 
the  same  capacity  and  should  fill  one  with  oxygen,  one  with  hydro- 
gen, one  with  carbon  dioxide,  one  with  marsh  gas,  and  so  on,  each 
being  at  the  same  temperature  and  exposed  to  the  same  pressure, 
then  each  would  contain  exactly  the  same  number  of  molecules. 

Suppose  one  of  these  cylinders  of  the  same  diameter  as  the 
others  should  be  twice  as  tall.  If  this  one  be  filled  with  gas  it  will, 
from  the  above,  contain  twice  as  many  molecules  as  the  others. 
Place  a  piston  in  the  mouth  of  this  cylinder  and  press  it  down  until 
the  volume  of  the  enclosed  gas  be  reduced  one-half,  that  is,  until 
it  becomes  the  same  as  that  of  the  other  cylinders.  The  space 
beneath  the  piston  now  contains  twice  as  many  molecules  as  the 
other  cylinders  contain.  From  Mariotte's  Law,  temperature 
remaining  constant,  the  volume  of  a  gas  varies  inversely  as  the 
pressure.  The  pressure  upon  the  compressed  cylinder  is  therefore 
twice  that  upon  the  others.  Hence  we  may  state,  as  a  corollary 
to  Avogadro's  law,  that  for  a  constant  temperature  and  volume,  the 
pressure  of  a  gas  varies  directly  as  the  number  of  molecules  enclosed. 

From  a  combination  of  Charles'  and  Mariotte's  Laws  it  is  shown 
that  for  constant  volume,  the  pressure  produced  by  an  enclosed 
gas  varies  as  the  absolute  temperature.  (The  absolute  tempera- 
ture is  obtained  by  adding  the  constant  273  to  the  temperature 
as  indicated  on  the  Centigrade  scale.)  We  therefore  see  that  the 
pressure  of  a  gas  confined  f in  a  given  volume  varies  (a)  with  the 
number  of  molecules  enclosed  and,  (b)  with  the  absolute  tempera- 
ture. 

257.  Decomposition  and  Dissociation. — In  general,  compound 
substances  if  heated  to  a  sufficiently  high  temperature  are  resolved 
into  simpler  ones.     If  when  these  simpler  substances  are  cooled 
to  the  primary  temperature  they  remain  separate,  the  original 
compound  body  is  said  to  have  undergone  decomposition.    On  the 
other  hand,  if  when  the  temperature  falls  the  simpler  substances 
recombine  and  reproduce  the  original  substance,  this  body  is  said 
to   have   undergone    dissociation.      Decomposition   is    therefore 
permanent  while  dissociation  is  transient  and  continues  only  so 
long  as  the  agency  which  brought  it  about  is  operative. 

258.  Example  of  Dissociation  by  Heat. — Ammonium  chloride, 
NH4C1,  like  other  ammonium  salts,  is  volatilized  with  compar- 


200  ELEMENTS  OF  ELECTRICITY. 

ative  ease.  Its  molecular  weight  being  53.5,  the  gas  produced  by 
the  volatilization  of  53.5  grams  should  exert  the  same  pressure 
as  that  produced  by  a  molugram  of  any  other  gas  confined  in  an 
equal  volume  and  at  the  same  temperature.  (A  molugram  is  the 
molecular  weight  expressed  in  grams,  as  for  example  2  grams  of 
hydrogen,  28  grams  of  nitrogen,  44  grams  of  carbon  dioxide,  and 
so  on.)  By  actual  experiment  however  the  pressure  is  found  to  be 
twice  as  great.  From  (a)  Par.  256  therefore,  there  must  be  twice 
as  many  molecules  present  in  the  gaseous  NH4C1  as  there  are  in 
the  other  gases.  The  explanation  is  that  the  NH4C1  has  been 
dissociated  by  the  heat,  each  molecule  becoming  two,  one  of 
ammonia,  NH3,  the  other  of  hydrochloric  acid,  HC1.  That  this 
is  so  may  be  proven  in  several  ways.  First,  if  NH4C1  became  a 
gas  without  dissociation,  the  specific  gravity  of  this  gas  referred 
to  hydrogen  should  be  26.7  while  it  is  actually  only  13.35  which 
is  the  specific  gravity  of  a  mixture  of  equal  volumes  of  NH3  and 
HC1.  Second,  the  specific  gravity  of  HC1  being  18.2  while  that 
of  NH3  is  only  8.5,  if  the  dissociation  takes  place  in  a  vertical 
closed  tube,  the  heavier  HC1  will  settle  at  the  bottom,  the  lighter 
NH3  rising  to  the  top.  If  by  means  of  a  stop  cock  at  the  middle 
of  the  tube  the  two  halves  be  now  cut  apart  and  after  cooling  be 
tested  separately,  the  contents  of  the  upper  half  will  be  found  to 
be  alkaline,  that  of  the  lower  half  acid. 

259.  Osmosis  and  Osmotic  Pressure. — Suppose  the  space 
below  the  piston  of  a  vertical  cylinder  to  be  filled  with  a  gas  under 
normal  pressure.  If  the  piston  be  raised,  thereby  increasing  the 
space  beneath  it,  the  gas  will  be  found  to  have  spread  through  this 
new  space  completely  filling  it.  There  is  therefore  a  force  or 
pressure  which  compels  a  volume  of  gas  to  diffuse  or  to  swell 
out  and  occupy  a  greater  space  when  it  has  the  opportunity  to 
do  so. 

Again,  if  in  the  bottom  of  a  vessel  there  be  placed  a  concen- 
trated solution  of  a  salt  and  if  then  there  be  poured  carefully  on 
top  of  this  solution  a  layer  of  pure  water,  in  a  short  while  the  dis- 
solved salt,  in  defiance  of  gravity,  will  have  spread  upward  and 
throughout  the  liquid  until  the  latter  is  all  of  a  uniform  density. 
By  using  a  colored  salt  the  progress  of  the  diffusion  can  be  easily 
observed.  There  is  therefore  a  force,  similar  to  the  gaseous  pres- 
sure described  above,  which  urges  the  particles  of  a  dissolved 
substance  to  spread  equally  throughout  the  solvent. 


VOLTAIC  ELECTRICITY. 


201 


There  are  known  various  membranes,  some  animal,  some 
vegetable,  and  some  artificial,  which  will  permit  the  passage 
through  them  of  certain  liquids  but  will  prevent  the  passage  of 
other  substances  dissolved  in  these  liquids.  On  account  of  this 
property  these  membranes  are  called  semi-permeable.  If  a  bladder 
(which  is  one  of  these)  be  filled  with  an  aqueous  solution  of  a  salt, 
tied  tightly,  and  then  submerged  in  a  vessel  of  pure  water,  it  will 
gradually  distend  and  may  finally  burst.  This  is  explained  by 
saying  that  the  substance  in  solution  is  urged  by  the  pressure 
described  above  to  spread  out  into  the  surrounding  solvent  but 
being  unable  to  pass  through  the  membrane  it  pushes  against  it 
and  distends  it,  thus  allowing  the  water  on  the  outside  to  enter. 
Although  this  explanation  is  admittedly  a  poor  one,  the  phenom- 
enon does  occur  and  is  called  osmosis,  and  the  force  exerted 
upon  the  membrane  by  the  dissolved  molecules  is  called  osmotic 
pressure. 

In  the  above  illustration  we  have  assumed  an  aqueous  solu- 
tion of  a  salt  but  under  proper  conditions  osmosis  takes  place 
whatever  the  nature  of  the  solvent  or  of  the  dissolved  sub- 
stance. 

260.  Demonstration  of  Osmotic  Pressure. — Osmotic  pressure 
may  be  conveniently  shown  as  follows.  A  membrane  is  stretched 
and  tied  over  the  mouth  of  a  glass  funnel  which  is  then  inverted 
and  filled  to  the  neck  with  a  solution,  say 
of  copper  sulphate.  The  inverted  funnel 
is  then  inserted,  as  shown  in  Fig.  117,  in  a 
vessel  of  pure  water  until  the  surface  of 
the  water  and  that  of  the  liquid  in  the 
neck  of  the  funnel  are  at  the  same  level. 
The  copper  sulphate  solution  will  be  ob- 
served to  rise  slowly  in  the  neck  of  the 
funnel  and  may  continue  to  do  so  for 
several  weeks,  attaining  its  maximum 
height  when  the  hydrostatic  pressure  of 
the  liquid  in  the  tube  just  prevents  the 
passage  of  additional  water  through  the 
membrane  and  the  further  dilution  of  the  Flg- 117- 

contained  solution.  The  osmotic  pressure  and  the  hydrostatic 
pressure  are  now  in  balance  and  by  measuring  the  latter  we 
determine  the  former. 


202  ELEMENTS  OF  ELECTRICITY. 

261.  Measurement  of  Osmotic  Pressure. — The  arrangement 
described  in  the  preceding  paragraph  is  not  well  suited  for  the 
measurement  of  osmotic  pressures.    These  are  relatively  great, 
The  osmotic  pressure  produced  by  a  dilute  solution  of  sugar  has 
driven  a  column  of  water  to  a  height  of  nearly  70  feet,  and  this 
pressure  is  frequently  exceeded.    The  membrane  would  not  stand 
these  pressures  and  it  is  impracticable  to  use  tubes  of  such  length. 
Again,  the  membrane  is  not  absolutely  impermeable  to  the  salt 
and  some  escapes  into  the  surrounding  solvent.    Also,  the  mem- 
brane is  distended,  thereby  increasing  the  volume  of  the  confined 
solution  and  materially  altering  the  degree  of  concentration.    For 
these  reasons  accurate  determinations  of  osmotic  pressure  were 
not  made  until  within  recent  years  when  it  was  discovered  that 
certain  colloidal  or  gelatinous  precipitates,  notably  the  ferro- 
cyanide  of  copper,  act,  so  far  as  permeability  is  concerned,  as 
ideal  membranes.    The  strength  of  a  film  of  such  a  precipitate  is 
however  very  small  and  in  order  that  it  may  withstand  the  pres- 
sure to  which  it  is  to  be  subjected  it  must  be  supported  in  some 
way.    This  object  is  now  attained  by  depositing  the  film  within  the 
substance  of  a  finely  porous  unglazed  porcelain  cup.    These  cups, 
about  two  inches  tall  and  three-quarters  of  an  inch  in  diameter, 
are  first  filled  with  a  solution  of  potassium  ferrocyanide  which 
slowly  soaks  into  the  walls.    They  are  then  immersed  in  a  solution 
of  copper  sulphate,  which  soaks  in  from  the  outside,  and  when  the 

.two  liquids  encounter  each  other  the  precipitate  is  formed.  The 
actual  process  requires  several  days'  time  and  involves  a  number 
of  precautions  not  necessary  to  mention  here.  Into  the  mouth  of 
the  prepared  cup  are  cemented  the  tube  up  which  the  liquid  is  to 
rise  and  a  second  tube  with  a  stop  cock  by  which  the  solution  is 
introduced.  The  vertical  or  pressure  tube  is  sealed  at  the  top  and 
the  osmotic  pressure  may  be  determined  by  the  amount  of  com- 
pression of  the  air  above  the  liquid.  In  practice,  the  pressure  tube 
is  a  mercurial  manometer.  By  using  these  closed  tubes  to  measure 
the  pressure,  the  amount  of  the  solvent  which  enters  the  cup  is 
reduced  to  a  minimum  and  the  concentration  of  the  solution  is 
altered  but  little. 

262.  Observations  of  Pfeffer. — The  botanist,   Pfeffer,   in  his 
investigations  in  plant  physiology,  made,  with  the  apparatus  just 
described,  a  series  of  observations  upon  the  osmotic  pressure  pro- 
duced under  various  conditions  by  dilute  solutions  of  organic 


VOLTAIC  ELECTRICITY.  203 

compounds  such  as  sugars,  alcohols,  etc.  His  results  were  pub- 
lished in  1877  but  at  that  time  attracted  no  special  attention  and 
it  remained  for  Arrhenius  and  Van't  Hoff  to  discover  some  ten 
years  later  the  value  of  his  data  and  its  bearing  upon  the  theory 
which  we  shall  shortly  explain. 

263.  Osmotic  Pressure  Varies  Directly  with  Number  of  Mole- 
cules Dissolved  in  Given  Volume  of  Solution. — Pfeffer  found 
that  for  these  dilute  solutions  the  osmotic  pressure  increased 
directly  with  the  strength  of  the  solution,  that  is,  if  the  concen- 
tration (and  hence  the  number  of  molecules  in  solution)  be 
doubled,  the  osmotic  pressure  is  likewise  doubled,  etc.  His 
results  for  cane  sugar  were  as  follows: 

Strength  of  Osmotic  •RotiVt  ^ 

Solution  Pressure  *vauo  g 

1%  510  mm.  510 

2%  1016  mm.  508 

4%  2082  mm.  520 

6%  3075  mm.  512 

In  this  table,  while  the  pressures  do  not  bear  to  each  other  the 
exact  theoretical  ratio,  the  variations  therefrom  are  not  greater 
than  are  to  be  expected  from  experimental  errors  and  from  the 
fact  that  the  observations  were  not  taken  under  precisely  the  same 
conditions  of  temperature,  although  they  were  made  within  a 
range  of  less  than  three  degrees  Centigrade. 

Comparing  different  substances,  he  found  that  while  the  osmotic 
pressure  of  a  one  per  cent  solution  of  cane  sugar  at  15.5°  C  was 
520.5  mm.,  that  of  a  one  per  cent  solution  of  raffinose  at  the  same 
temperature  was  only  299  mm.  The  relation  between  these  two 
numbers  was  not  discovered  until  subsequent  investigators 
worked  upon  his  data.  The  formula  for  cane  sugar  is  C^H^On 
and  its  molecular  weight  is  342 ;  that  for  raffinose  is  Ci8H32Oi65H20 
and  its  molecular  weight  is  594.  Therefore,  equal  weights  of  the 
two  do  not  contain  the  same  number  of  molecules,  a  one  per  cent 
solution  of  raffinose  containing  fewer  than  a  one  per  cent  solution 
of  sugar.  Let  us  see  how  the  pressures  compare  if  we  take  the 
same  number  of  molecules  of  each.  Each  litre  of  his  cane  sugar 
solution  contained  ^  °f  a  molugram.  The  same  fraction  of  a 
molugram  of  raffinose  would  be  ^W  of  594  or  17.37  grams.  If 
10  grams  produced  a  pressure  of  299  mm.,  what  pressure  would 
17.37  produce?  10  :  299  :  :  17.37  :  x 


204  ELEMENTS  OF  ELECTRICITY. 

whence  x  =  519.4  mm.  as  compared  to  the  520.5  mm.  of  the  sugar 
solution. 

This  and  other  examples  show  that  substances  in  solution  con- 
form to  Avogadro's  Law  and  to  its  corollaries,  that  is,  equal 
volumes  of  solutions  which  at  the  same  temperature  exhibit  the 
same  osmotic  pressure  contain  the  same  number  of  dissolved 
molecules,  and  also,  other  conditions  being  constant,  the  osmotic 
pressure  varies  directly  with  the  number  of  molecules  in  solution. 

264.  Osmotic  Pressure  Follows  Mariotte's  Law. — An  exami- 
nation of  Pfeffer's  data  will  reveal  the  fact  that  osmotic  pressure 
also  follows  the  corollary  to  Mariotte's  Law  for  gaseous  pressure, 
that  is,  other  conditions  being  constant  the  osmotic  pressure 
varies  directly  with  the  absolute  temperature.    For  example,  the 
osmotic  pressure  of  a  one  per  cent  solution  of  sugar  at  14.15°  C  is 
510  mm.  and  at  32°  C  is  544  mm.    Applying  the  law  to  the  lower 

pressure 

510  :  z=273+14.15  :  273+32 

whence  x  =  541.7  mm., 
agreeing  closely  with  the  observed  pressure  544  mm. 

265.  Osmotic    Pressure   of  a    Molecule   in    Solution    Equals 
Pressure  of  a  Gaseous  Molecule  under  Equal  Volume  and  Tem- 
perature.— We  have  seen  from  Par.  263  above  that  -£&  of  a  molu- 
gram of  sugar  or  of  other  organic  substance  dissolved  in  a  litre  of 
water  exerts  at  15.5°  C  an  osmotic  pressure  of  about  520  mm.    Let 
us  see  what  pressure  the  same  fraction  of  a  molugram  (and  hence 
the  same  number  of  molecules)  of  hydrogen  confined  in  the  same 
space  and  at  the  same  temperature  would  exert.     One  gram  of 
hydrogen  at  0°  C  and  760  mm.  measures  11.165  litres,  therefore,  a 
molugram  of  hydrogen  (2  grams),  would  under  these  conditions 
occupy  22.33  litres,  and  ^W  of  a  molugram  would  occupy  .6529 
litre.    At  a  temperature  of  15.5°  C  this  would  dilate  to  .6914 
litre  and  if  this  be  allowed  to  expand  into  the  space  of  1.006  litres 
(the  space  occupied  by  one  litre  of  water  to  which  10  grams  of 
sugar  is  added),  the  pressure  would  drop  according  to  the  propor- 
tion 

760  :  x  =  1.006  :  .6914 

whence  x  =  522 .4  mm. 

We  see  then  that  the  osmotic  pressure  of  the  sugar  in  solution 
is  the  same  as  the  pressure  exerted  by  an  equal  number  of  mole- 


VOLTAIC  ELECTRICITY.  205 

cules  of  gas  confined  in  the  same  space  and  at  the  same  tem- 
perature. 

266.  Van't  HofTs  Generalization. — A  consideration  of  the  fore- 
going facts  led  to  the  generalization  by  Van't  Hoff  which  is  to  the 
effect  that  "the  osmotic  pressure  of  a  substance  in  solution  is  the 
same  as  the  gas  pressure  which  would  be  observed  if  the  dissolved 
substance  alone,  in  gaseous  state  and  at  the  same  temperature, 
occupied  the  volume  of  the  solution."    In  other  words,  these  sub- 
stances in  solution  behave,  comparing  osmotic  pressure  to  gaseous 
pressure,  precisely  as  if  they  had  been  converted  into  a  gas  and 
filled  alone  the  space  occupied  by  the  solution. 

Independent  theoretical  considerations  based  upon  the  lowering 
of  the  freezing  point  and  the  raising  of  the  boiling  point  by  sub- 
stances in  solution  lead  to  the  same  conclusions  and  entirely 
corroborate  Van't  Hoff. 

267.  Exceptions  to  Van't  Hoflf's  Generalization.— Van't  HofFs 
generalization  applies,  as  we  have  seen,  to  dilute  solutions  of 
organic  compounds.     If  the  solutions  become  concentrated,  the 
laws  of  osmotic  pressure  no  longer  hold  strictly.    This  is  thought 
to  be  parallel  to  the  failure  of  gases,  as  they  approach  their  point 
of  condensation,  to  follow  the  laws  of  Charles  and  Boyle. 

If,  now,  we  turn  our  attention  to  solutions  of  the  inorganic 
compounds  we  find  that  the  majority  of  them  are  exceptions  and 
give  osmotic  pressures  in  excess  of  those  required  by  theory. 
These  exceptions  embrace  solutions  of  all  the  acids,  all  the  bases 
and  all  the  salts.  It  might  seem  therefore  that  in  announcing  as 
general  a  law  to  which  the  exceptions  outnumber  the  agreements, 
Van't  Hoff  had  overstepped  the  bounds  of  prudence. 

268.  Dissociation  Theory  of  Arrhenius. — In  Par.  263  above 
we  saw  that  osmotic  pressure  varied  directly  with  the  number  of 
molecules  in  solution.    Since  in  the  exceptional  cases  the  pressure 
is  always  greater  than  what  it  should  be  in  theory,  there  must  be 
a  greater  number  of  molecules  present  in  solution  than  is  indicated 
by  the  weights  taken.     To  account  for  this  greater  number, 
Arrhenius  advanced  the  theory  that  just  as  the  excessive  pressure 
produced  by  iodine,  ammonium  chloride,  etc.,  when  converted 
into  vapor  is  explained  by  the  fact  that  these  substances  are  dis- 
sociated by  the  heat  employed,  so  the  excessive  osmotic  pressures 
are  to  be  explained  by  the  fact  that  the  substances  in  solution 


206  ELEMENTS  OF  ELECTRICITY. 

undergo  dissociation,  or  ionization,  that  is,  split  up  into  a  greater 
number  of  parts.  It  is  also  a  part  of  his  theory  that  these  part 
molecules  or  ions,  whether  they  be  atoms  or  compound  radicles, 
exert  the  same  osmotic  pressure  as  an  undissociated  molecule. 
Some  of  the  consequences  following  from  this  theory  were  so 
startling  and  so  contrary  to  the  views  generally  held  by  chemists 
that  it  was  at  first  vigorously  combated  and  reluctantly  accepted 
as  one  by  one  the  objections  advanced  against  it  were  explained 
away.  A  full  exposition  of  these  consequences  and  replies  to  the 
objections  would  require  an  extended  treatise.  We  can  here  do 
but  little  more  than  allude  to  a  few  of  those  most  obviously  con- 
nected with  our  subject. 

269.  Why  Ionization  Takes  Place  in  Solution. — Salts,  acids 
and  bases  consist  of  two  parts,  a  metal  or  hydrogen  (or  a  radicle 
playing  a  similar  part)  combined  with  an  acid  radicle  or,  in  the 
case  of  the  base,  with  hydroxyl.    The  metal  or  hydrogen  portion 
carries  a  positive  charge  of  electricity;  the  remaining  radicle 
carries  an  equal  negative  charge.    These  two  parts  may  therefore 
be  regarded  as  held  together  by  the  attraction  of  these  opposite 
charges.    The  charges  being  relatively  great  (Par.  278)  and  the 
distance  separating  the  parts  being  infinitely  small,  the  attraction 
is  very  great  (Par.  53).    In  Par.  90  we  saw  that  if  two  charged 
bodies  which  in  air  attract  or  repel  each  other  with  a  certain  force 
were  placed  in  some  other  medium  whose  dielectric  coefficient  is 
K,  then  the  force  exerted  between  the  two  bodies  would  be  only 
^th  of  what  it  was  in  air.    The  dielectric  coefficient  of  water  is 
given  in  Par.  92  as  80,  or  with  the  exceptions  of  hydrogen  peroxide 
and  hydrocyanic  acid,  greater  than  that  yet  determined  for  any 
other  substance.    The  force  which  held  the  ions  together  is  there- 
fore reduced  to  ^th  of  itself  when  the  substance  is  brought  into 
solution,  and  the  ions  drift  apart.    This  view  is  corroborated  by 
the  variation  in  dissociation  produced  by  using  solvents  of  dif- 
ferent dielectric  coefficients. 

270.  How    Ionization    Takes    Place. — Ionization    takes   place 
differently  from  the  dissociation  by  heat.     The  metallic  salts 
split  into  the  metal  and  the  acid  radicle;  the  acids  split  into  hydro- 
gen and  the  acid  radicle;  the  bases  split  into  the  metal  and  the 
hydroxyl  radicle.    Now  such  radicles  as  NH4,  OH,  S04,  etc.,  which 
this  requires,  are  unknown  as  separate  entities.    The  ionization  of 


VOLTAIC  ELECTRICITY.  207 

KC1  supposes  the  presence  in  the  water  of  atoms  of  potassium 
and  of  chlorine.  If  this  be  so,  some  of  the  chlorine  should  reveal 
itself  by  its  color  and  odor.  Further,  it  is  well  known  that  potas- 
sium placed  upon  water  decomposes  it  with  such  violence  as  to 
produce  flame  and  forms  potassium  hydroxide.  None  of  these 
effects  are  produced  and  this  was  once  regarded  as  a  grave  objec- 
tion to  the  theory.  This  objection  is  answered  by  the  statement 
that  ions  carrying  electrical  charges  differ  from  those  that  do  not. 
A  metallic  ion  can  go  into  solution  only  when  it  has  a  positive 
charge,  and  once  in  solution  it  can  not  be  withdrawn  until  this 
.charge  is  removed  or  neutralized.  This  can  be  shown  experi- 
mentally thus.  A  plate  of  zinc  dipped  into  hydrochloric  acid  is 
attacked  vigorously  and  goes  into  solution.  If,  however,  this  plate 
be  charged  negatively,  the  action  of  the  acid  immediately  ceases. 
So  long  as  the  potassium  ion  carries  a  positive  charge  it  remains 
in  solution,  but  when  this  charge  is  withdrawn  by  contact  with  the 
negatively-charged  cathode  the  potassium  regains  its  usual  proper- 
ties and  decomposes  the  water.  It  is  interesting  to  note  that  over 
one  hundred  years  ago  Davy  conjectured  that  "in  this  state  of 
transition  or  electrical  progression  the  chemical  elements  are 
deprived  of  their  wonted  properties,  their  affinities  being  rendered 
dormant  or  counteracted  by  the  predominating  influence  of  the 
electrical  attraction." 

271.  lonization  Incomplete. — Should  NaCl  in  solution  be  com- 
pletely ionized,  the  osmotic  pressure  produced  would  be  twice 
that  produced  by  an  equal  number  of  molecules  of  sugar.    Barium 
chloride,  BaCl2,  since  it  ionizes  into  Ba,  Cl,  Cl,  should  produce 
three  times  this  pressure.     Were  this  the  case,  doubts  about 
Arrhenius'  theory  would  disappear,  but  it  is  not  the  case.    The 
osmotic  pressure  of  NaCl  is  not  twice  that  of  a  sugar  solution  of 
the  same  molecular  concentration.    The  explanation  is  that  these 
salts  do  not  completely  ionize.    At  ordinary  temperatures  moder- 
ately dilute  solutions  of  salts,  strong  acids  and  strong  bases  ionize 
from  80  to  90  per  cent.    However,  as  the  dilution  increases  so  does 
the  dissociation  and  it  approaches  the  theoretical  figure  when  the 
dilution  reaches  one  molugram  per  1000  litres. 

272.  Experimental  Demonstration  of  Free  Ions. — The  presence 
of  free  ions  was  shown  by  Ostwald  in  the  following  experiment. 
A  horizontal  glass  tube  (Fig.  118)  about  one-half  inch  in  diameter 


208 


ELEMENTS  OF  ELECTRICITY. 


and  some  20  inches  long  is  bent  up  at  right  angles  at  the  ends, 
these  terminal  portions  being  expanded  to  the  size  of  a  test  tube 
and  a  piece  of  platinum  wire  C  being  fused  through  the  bottom  of 
the  end  B.  The  tube  is  filled  with  dilute  sulphuric  acid.  In  the 
end  A  is  inserted  a  rubber  stopper  through  which  passes  an 


Fig.  118. 


amalgamated  rod  of  pure  zinc.  In  the  end  B  is  inserted  a  stopper 
carrying  a  slender  glass  manometer  M  which  is  filled  with  water, 
colored  for  ease  of  observation.  The  zinc  rod  is  connected  to  the 
positive  pole  of  a  battery  of  five  or  six  cells,  D;  the  platinum  wire 
C  is  connected  through  the  key  K  to  the  negative  pole.  The 
instant  the  key  is  closed,  the  manometer  indicates  an  increase  of 
pressure  in  B  due  to  the  hydrogen  released  at  C. 

Just  before  the  key  was  closed  this  hydrogen  must  have  existed 
in  the  immediate  vicinity  of  C  in  the  form  of  free  ions.  From  Par. 
270  they  must  have  carried  positive  charges.  But  the  cathode  C 
was  also  positively  charged  and  these  ions  were  therefore  repelled. 
As  soon,  however,  as  the  key  was  closed,  the  charge  on  C  was 
withdrawn,  the  hydrogen  ions  moved  up  to  C,  gave  up  their 
charges  and  then  recovered  their  status  as  free  hydrogen  atoms. 

273.  Ions  Not  from  Same  Molecule. — According  to  the  older 
theories,  when  the  circuit  was  closed  the  zinc  and  sulphuric  acid 
in  A  reacted,  producing  zinc  sulphate  and  hydrogen  and  this 
hydrogen  travelled  from  A  to  B  and  appeared  at  C. 

The  following  considerations  will  show  that  it  is  impossible  that 


VOLTAIC  ELECTRICITY.  209 

the  hydrogen  atoms  released  in  A  should  be  instantly  shot  across 
the  15  or  20  inches  of  electrolyte  to  C.  By  moderate  exertion  a 
small  lead  ball  may  be  thrown  several  hundred  feet.  If  this  ball 
be  cut  up  into  fine  shot  the  force  required  to  throw  it  to  this  dis- 
tance would  be  very  much  greater.  If  it  be  reduced  to  dust  we 
could  not  command  sufficient  force,  and  a  particle  of  dust  might 
contain  several  million  atoms.  Finally,  the  hydrogen  atom  is  over 
200  times  lighter  than  the  lead  atom  and  instead  of  moving 
through  air  moves  through  the  liquid.  It  is  thus  seen  that  the 
force  required  would  be  beyond  all  reason. 

As  a  matter  of  fact,  the  ions  move  from  both  electrodes  in 
opposite  directions  and  at  different  rates  of  speed.  These  rates 
have  been  accurately  measured.  The  swiftest  of  the  ions,  the 
hydrogen,  moves  under  ordinary  conditions  a  little  faster  than 
one-thousandth  of  an  inch  per  second. 

274.  Grotthus'  Theory. — We  have  already  mentioned  (Par.  195) 
that  no  signs  of  the  moving  ions  can  be  seen  between  the  electrodes. 
Grotthus  in  1805  attempted  to  explain  this  by  the  theory  that 
there  was  an  exchange  of  hydrogen  atoms  from  molecule  to  mole- 
cule of  the  acid  between  the  electrodes,  just  as  each  individual  in  a 
bucket  chain  at  a  fire  passes  a  bucket  to  the  person  on  one  side 
of  him  and  receives  a  bucket  from  the  person  on  the  other  side. 
The  correct  explanation  is  that  so  long  as  these  ions  carry  charges 
they  do  not  possess  their  ordinary  properties  and  do  not  aggregate 
into  visible  masses. 

275.  Electrolytes  and  Non-Electrolytes. — In  Par.  267  we  saw 

that  solutions  of  all  the  acids,  all  the  bases,  and  all  the  salts,  and 
only  these,  produce  osmotic  pressures  in  excess  of  those  called  for 
by  theory.  From  what  has  been  brought  out  in  the  preceding 
pages,  the  student  will  now  be  prepared  for  our  final  and  most 
startling  generalization,  namely,  those  and  only  those  solutions 
which  produce  abnormal  osmotic  pressure  conduct  electricity  or 
are  electrolytes.  All  other  solutions  are  non-conductors  or  non- 
electrolytes. 

276.  Electrolytic  Properties  Depend  Upon  lonization. — Since 
the  common  property  of  these  solutions,  excessive  osmotic  pres- 
sures, has  been  shown  to  result  from  ionization,  it  is  but  natural 
to  assume  that  their  electrolytic  property  has  the  same  cause.    A 
vast  accumulation  of  facts  points  to  this  same  conclusion. 


210  ELEMENTS  OF  ELECTRICITY. 

Sulphuric  acid  when  free  from  water  is  a  non-conductor.  Per- 
fectly pure  water  is  also  a  non-conductor.  Such  water  never 
exists  in  nature  and  perhaps  may  never  be  prepared,  but  by  a 
special  treatment  to  remove  dissolved  gases,  and  a  final  distillation 
in  vacuo,  water  has  been  prepared  of  such  purity  that  a  column 
of  it  one  millimeter  (one  twenty-fifth  of  an  inch)  long  had  the 
same  resistance  as  a  copper  wire  of  the  same  diameter  but  en- 
circling the  earth  at  the  equator  300  times.  A  solution  of  sulphuric 
acid  in  water  is,  however,  a  very  good  conductor. 

Again,  since  we  have  seen  (Par.  271)  that  ionization  increases 
with  dilution,  a  dilute  solution,  the  amount  of  dissolved  substance 
being  kept  constant,  should  conduct  better  than  a  strong  one, 
and  this  is  found  to  be  the  case. 

A  solution  of  hydrochloric  acid  in  water  is  a  very  good  con- 
ductor; a  solution  of  the  same  in  chloroform,  no  ionization  taking 
place,  is  a  non-conductor.  Such  examples  may  be  multiplied 
indefinitely. 

277.  Vapor  Tension. — In  Par.  259  illustrations  were  given  of 
the  force  or  pressure  which  causes  gases  to  diffuse  through  space, 
and  dissolved  substances  to  spread  through  unoccupied  solvent. 
This  tendency  to  diffuse  is  general.    If  a  liquid  be  introduced 
beneath  a  bell  jar,  a  portion  of  the  liquid  passes  into  a  state  of 
vapor  and  fills  the  jar  and  the  evaporation  continues  until  the 
pressure  of  the  vapor  above  the  liquid  balances  the  force  which 
tends  to  throw  off  the  liquid  into  space.    To  this  force  the  name 
vapor  tension  has  been  applied.    It  is  to  be  noted  that  in  order  to 
pass  from  a  liquid  to  a  vapor  a  certain  amount  of  heat  must  be 
taken  in  by  the  vapor.    The  vapor  passes  off  accompanied  by  this 
latent  heat  which  is  necessarily  lost  by  the  liquid  left  behind. 

278.  Solution  Tension. — Nernst  advanced  the  theory  that  a 
similar  state  of  affairs  obtains  for  solids  immersed  in  liquids,  that 
is,  there  is  a  force,  designated  by  him  solution  tension,  which  tends 
to  drive  particles  of  the  solids  off  into  solution  in  the  liquid.    We 
have  seen  (Par.  270)  that  a  metallic  ion  can  go  into  solution  only 
when  it  carries  with  it  a  positive  charge.    Therefore,  parallel  to 
the  heat  in  the  case  of  the  vapor,  the  liquid  about  a  metallic  plate 
becomes  positively  charged  and  the  plate  becomes  correspond- 
ingly negatively  charged.    Ions  continue  to  be  thrown  off  from  the 
metal  until  the  force  throwing  them  off,  or  the  solution  tension, 


VOLTAIC  ELECTRICITY.  211 

is  just  counterbalanced  by  the  contrary  force  of  attraction  which 
tends  to  pull  the  positively  charged  ions  back  to  the  negatively 
charged  plate.  To  this  theory  the  objection  was  advanced  that 
if  a  metal  plate  threw  off  ions  it  would  lose  weight  but  in  many 
cases  no  such  loss  can  be  detected  by  even  the  most  delicate 
measurements.  The  reply  to  this  is  that  the  quantity  of  elec- 
tricity carried  by  the  ions  is  so  great  that  equilibrium  is  reached 
long  before  there  passes  into  solution  enough  ions  to  be  detected 
by  our  most  refined  methods  of  weighing.  For  example,  to  carry 
into  solution  31.8  grams  of  copper  would  require  96,540  coulombs 
(Par.  231)  and  to  carry  in  only  one-thousandth  of  a  gram  (the 
smallest  amount  that  can  be  weighed  in  an  ordinary  analytical 
balance)  would  require  over  three  coulombs,  each  of  which  is 
about  three  billion  electrostatic  units  (Par.  228). 

279.  Theory  Applied  to  the  Simple  Cell. — Consider  the  case 
of  the  simple  cell  (Par.  193).    Both  the  zinc  and  the  copper  throw 
off  ions  into  the  electrolyte  but  the  zinc  has  the  greater  tendency 
to  pass  into  solution  therefore  more  zinc  ions  go  into  solution  and 
the  zinc  plate  becomes  more  negatively  charged  than  the  copper 
plate.     The  result  is  that,  as  compared  to  the  zinc  plate,  the 
copper  plate  is  positively  charged.    When  these  plates  are  con- 
nected through  the  external  circuit,  the  current  flows  from  the 
copper  to  the  zinc,  the  negative  charge  on  the  zinc  is  partly  neu- 
tralized and  the  zinc  plate  can  therefore  throw  more  ions  into 
solution,  and  so  on. 

280.  Atomic  Character  of  Electricity. — We  have  seen  above 
that  the  passage  of  a  given  quantity  of  electricity  through  an 
electrolyte  always  releases  equivalent  weights  of  ions.     Since 
96,540  coulombs  liberate  one  gram  of  hydrogen  and  107.9  grams 
of  silver,  and  since  this  ratio  is  constant  no  matter  how  many 
coulombs  flow  through  the  electrolyte,  the  quantity  of  electricity 
that  would  release  one  microcrith  of  hydrogen  would  also  release 
107.9  microcriths  of  silver,  that  is,  the  quantity  that  releases  one 
atom  of  hydrogen  releases  one  atom  of  silver  and  one  atom  of  any 
other  univalent  element.    Since  the  quantity  of  electricity  which 
releases  an  ion  is  equal  to  the  charge  which  the  ion  carries,  we  see 
that  all  univalent  ions  carry  equal  charges,  either  positive  or 
negative.    Bivalent  ions  carry  twice  the  charge  of  univalent  ions, 
and  trivalent  ions  carry  three  times  this  charge,  and  so  on.    Every 


212        .  ELEMENTS  OF  ELECTRICITY. 

unit  of  valency  therefore  is  accompanied  by  the  same  definite 
quantity  of  electricity,  either  positive  or  negative,  and  since  there 
are  no  fractions  of  these  charges  and  they  vary  by  whole  numbers, 
or  in  simple  ratio,  Helmholtz  concluded  that  electricity  was 
divided  into  elementary  portions  or  atoms.  These  electrical  atoms 
which  accompany  ions  have  been  named  electrons.  Assuming 
that  an  ion  and  an  atom  of  hydrogen  are  the  same,  the  electron 
has  been  calculated  as  2.4xlO~10  electrostatic  units. 

281.  Extensive  Scope  of  Theory  of  Electrolytic  Dissociation.— 

The  scope  of  the  theory  of  electrolytic  dissociation  is  extensive. 
Its  applications  to  pure  chemistry  are  even  more  wonderful  than 
those  that  we  have  just  considered.  It  explains  why  water  is  one 
of  the  products  of  most  chemical  reactions;  why  the  majority  do 
not  take  place  unless  water  be  present;  why,  for  example,  dry 
sulphuric  acid  has  no  effect  upon  blue  litmus;  why  dry  hydro- 
chloric acid  does  not  react  with  dry  ammonia;  why  dry  sulphuric 
acid  does  not  attack  dry  sodium.  It  also  explains  such  facts  as 
why  silver  chloride  is  precipitated  by  the  soluble  chlorides  yet 
not  by  the  chlorates;  why  KOH  precipitates  metallic  hydroxides 
yet  CH3OH  does  not,  etc.,  etc.  The  statement  is  even  made, 
though  not  yet  universally  accepted,  that  no  metathetical  reaction 
is  possible  unless  preceded  by  ionization  either  by  solution,  by 
fusion,  or  by  vaporization.  It  is  being  developed  by  many  inves- 
tigators and  there  is  every  reason  to  believe  that  remaining  ob- 
jections which  may  be  advanced  against  it  will  shortly  be  explained 
away. 


VOLTAIC  ELECTRICITY. 


213 


CHAPTER  24. 

RESISTANCE. 

282.  Resistance. — For  the  beginner  it  is  helpful  in  forming  a 
physical  conception  of  certain  electrical  phenomena  to  think  of 
electro-motive  force  as  a  pressure  which  drives  or  pushes,  or  tends 
to  drive  or  push,  electric  charges.    If  two  points  between  which 
there  exists  a  difference  of  potential  be  connected  by  a  conductor, 
the  electro-motive  force  will  cause  a  flow  of  electricity  from  the 
point  of  higher  potential  to  that  of  lower,  and  the  greater  the 
difference  in  potential  between  the  two  points  the  greater  the 
pressure  and  the  greater  the  quantity  of  electricity  that  will  flow 
across  in  a  given  time.    This  movement  is  also  affected  by  the 
nature  of  the  conductor  between  the  two  points.    For  example, 
it  takes  a  longer  time  for  a  given  quantity  of  electricity  to  flow 
through  a  long  thin  wire  than  it  does  through  a  short  thick  one.. 
We  have  seen  (Par.  228)  that  the  current  is  measured  by  the 
quantity  of  electricity  flowing  past  a  given  point  in  a  unit  of  time, 
hence  the  current  in  the  long  thin  wire  is  smaller  than  that  in  the 
short  thick  wire.     The  long  thin  wire  therefore  cuts  down  or 
reduces  the  current  by  obstructing  its  flow.     This  hindrance 
which  the  wire  offers  to  the  flow  is  called  its  resistance. 

283.  Example  of  Effect  of  Resistance. — The  following  experi- 
ment will  show  the  effect  of  resistance.     Fig.   119  represents 
diagrammatically  a  cell  or  battery  A  and  in  the  external  circuit 

B  c 


Fig.  119. 

two  copper  voltameters  D  and  E.    When  the  key  K  is  closed  the 
current  from  the  cell  divides  at  B,  a  part  going  through  the  upper 


214  ELEMENTS  OF  ELECTRICITY. 

voltameter  Z),  and  the  remainder  through  the  lower  voltameter  E. 
The  electro-motive  force  which  drives  the  current  through  the 
two  voltameters  is  precisely  the  same,  since  it  is  due  to  the  dif- 
ference of  potential  between  B  and  C,  but  in  the  upper  voltameter 
it  has  to  drive  it  through  the  short  stout  wire  and  in  the  lower  volt- 
ameter it  has  to  drive  it  through  the  longer  and  thinner  wire.  If 
the  key  be  kept  closed  for  a  convenient  time  and  then  opened  and 
the  cathodes  be  weighed,  it  will  be  found  that  the  cathode  of  D 
has  increased  considerably  more  in  weight  than  that  of  E,  hence 
a  greater  quantity  of  electricity  has  passed  through  D  in  the  given 
time,  that  is,  the  current  through  D  has  been  greater  than  that 
through  E. 

284.  The  Practical  Unit  of  Resistance,  the  Ohm.—  This  sub- 
ject was  investigated  first  by  Ohm  who  showed  that  the  resistance 
of  a  given  conductor  of  uniform  cross-section  varies  directly  as 
its  length  and  inversely  as  the  area  of  its  cross-section.    At  the 
time  when  he  carried  on  his  researches  there  were  no  units  of 
resistance  and  he  therefore  extemporized  standards  by  means  of 
definite  lengths  of  wire  of  a  given  size  which,  for  the  sake  of  com- 
pactness, he  wrapped  up  into  coils.    He  used  these  resistance  coils 
himself  and  distributed  others  among  those  of  his  scientific  friends 
who  wished  to  verify  his  results. 

The  practical  unit  of  resistance,  the  ohm,  is  named  in  his  honor 
and  will  be  defined  later  (Par.  291)  ;  for  the  present  we  must  con- 
tent ourselves  with  the  statement  that  it  is  about  the  resistance 
of  a  piece  of  ordinary  iron  telegraph  wire,  one-sixth  of  an  inch  in 
diameter  and  one  hundred  yards  long;  or  about  the  resistance  of 
ten  feet  of  annealed  copper  wire  one-hundredth  of  an  inch  in 
diameter. 

285.  Laws  of  Resistance.  —  We  saw  above  that  Ohm  showed 
that  the  resistance  of  a  conductor  of  uniform  cross-section  varies 
directly  as  its  length  and  inversely  as  the  area  of  its  cross-section. 
He  also  showed  that  it  depends  upon  the  material  of  which  the 
conductor  is  composed.    If  R  represent  the  resistance  of  such  a 
conductor,  this  law  may  be  expressed 


in  which  I  is  the  length  of  the 
conductor,  s  is  the  area  of  its  cross-section,  and  p  is  a  factor 


VOLTAIC  ELECTRICITY.  215 

depending  upon  the  material  and  called  its  specific  resistance. 
Resistance  also  varies  with  the  temperature  of  the  conductor. 

In  addition  to  the  foregoing,  there  are  a  few  substances  whose 
resistance  varies  under  certain  conditions  in  an  anomalous  man- 
ner. For  example,  when  bismuth  is  placed  in  a  magnetic  field  its 
resistance  increases;  when  selenium  is  exposed  to  light  its  resist- 
ance decreases.  The  resistance  of  some  substances,  notably 
carbon,  decreases  with  pressure.  The  prime  factors  of  the  resist- 
ance of  a  conductor,  however,  are  length,  area  of  cross-section, 
material  and  temperature  and  these  we  shall  now  consider  in 
detail. 

286.  Resistance  Varies  Directly  with  Length  of  Conductor. — 
This  statement  requires  no  amplification.     The  principle  has 
numberless  applications.    By  measuring  the  resistance  of  a  foot 
of  a  given  wire  we  can  easily  calculate  the  resistance  of  any  speci- 
fied length  of  it.    To  determine  the  length  of  a  submarine  cable 
coiled  upon  a  reel,  it  is  not  necessary  to  unwind  it.    We  measure 
its  total  resistance,  obtain  by  measurement  or  from  a  table  the 
resistance  of  the  wire  per  foot,  whence  we  get  at  once  the  total 
number  of  feet. 

If  conductors  of  different  lengths,  cross-sections  or  materials 
be  connected  one  after  the  other,  or  in  series,  the  total  resistance 
of  the  resulting  conductor  is  the  sum  of  the  separate  resistances. 

287.  Resistance  Varies  Inversely  as  Area  of  Cross- Section  of 
Conductor. — The  resistance  of  a  conductor  varies  inversely  as  the 
area  of  its  cross-section,  that  is,  the  greater  this  area,  the  less  the 
resistance  and  the  less  this  area,  the  greater  the  resistance.    For 
the  usual  current  electricity  it  is  unaffected  by  the  geometrical 
shape  of  the  cross-section,  and  whether  this  be  circular  or  square 
or  irregular  or  tube  like,  if  the  area  be  the  same  the  resistance  is 
the  same.    The  resistance  of  a  wire  cable  of  many  strands  is  the 
same  as  that  of  a  single  conductor  whose  cross-section  is  equal  to 
the  sum  of  the  cross-sections  of  the  separate  strands.    Since  wires 
are  usually  circular  in   cross-section,   the   resistances  of  equal 
lengths  of  wire  of  the  same  material  are  to  each  other  inversely  as 
the  squares  of  the  diameters  of  the  wires. 

288.  Specific  Resistance. — If  in  the  expression  (Par.  285)  for 
the  resistance  of  a  conductor 


216  ELEMENTS  OF  ELECTRICITY. 

we  make  I =one  centimeter  and  s  =  one  square  centimeter,  we  have 

R  =  P 

'  But  p  is  the  specific  resistance  of  the  material  of  which  the 
conductor  is  composed,  whence  we  see  that  this  specific  resistance 
is  measured  by  the  resistance  of  a  centimeter  cube  of  the  substance 
or  of  a  prism  or  cylinder  whose  cross-section  is  one  square  centi- 
meter and  whose  length  is  one  centimeter.  The  resistance  of  a 
piece  of  metal  of  this  size  is  so  small  that  it  is  usually  expressed 
in  millionths  of  an  ohm,  or  microhms.  For  example,  the  specific 
resistance  of  silver,  which  is  the  least,  is  about  1.5  microhms,  that 
of  copper  about  1.6,  that  of  brass  about  7,  that  of  wrought  iron 
10  to  15,  that  of  lead  about  20,  that  of  mercury  about  95,  that  of 
cast  iron  over  100.  On  the  other  hand,  the  specific  resistance  of 
the  ordinary  electrolytes  runs  from  1  to  30  ohms  while  the  specific 
resistance  of  lead  glass  is  given  as  84  trillion  ohms  and  that  of 
flint  glass  is  two  hundred  thousand  times  greater. 

289.  Variation  of  Resistance  with  Temperature. — The  resist- 
ance of  all  substances  changes  as  their  temperature  varies.  The 
resistance  of  the  metals  increases  as  their  temperature  rises;  on 
the  other  hand,  the  resistance  of  electrolytes  and  of  most  non- 
metals  decreases  with  increase  in  temperature.  This  is  of  especial 
importance  in  the  case  of  carbon.  The  resistance  of  the  carbon 
filament  in  an  incandescent  lamp  when  hot  and  giving  light  is 
very  nearly,  if  not  quite,  fifty  per  cent  less  than  when  cold. 

The  amount  of  change  in  resistance  per  ohm  per  degree  is 
called  the  temperature  coefficient.  The  metals  therefore  have  a 
positive  temperature  coefficient;  the  non-metals  and  electrolytes 
have  a  negative  coefficient.  Starting  at  0°  C,  the  resistance  of 
many  metals  decreases  about  ?^d  for  every  drop  of  1°  C.  At  this 
rate  their  resistance  would  entirely  vanish  at  —273°  C,  which  is 
the  absolute  zero  of  temperature  as  deduced  from  Charles'  law  of 
gaseous  pressure.  It  is  interesting  to  find  this  significant  tempera- 
ture thus  indicated  by  an  independent  deduction.  It  must  be 
noted  however,  that  recent  experiments  show  that  at  the  tempera- 
ture of  liquid  air  the  resistances  no  longer  decrease  at  the  same 
rate. 

It  is  highly  desirable  that  we  should  be  able  to  prepare  standards 
of  resistance  which  would  be  independent  of  temperature,  and 
certain  alloys  have  been  discovered  whose  temperature  coefficient 


VOLTAIC  ELECTRICITY.  217 

is  so  small  that  for  most  purposes  it  may  be  neglected.  Typical 
of  these  is  manganin,  composed  of  84  parts  copper,  4  parts  nickel 
and  12  parts  manganese. 

290.  The  Platinum  Thermometer.— This  change  of  resistance 
with  temperature  is  utilized  in  the  construction  of  certain  forms 
of  pyrometers,  thermometers  for  the  measurement  of  temperatures 
beyond  the  range  of  the  mercurial  thermometer  or  extending  up 
to  1000°  C.    In  most  of  these  a  platinum  wire  is  wrapped  around 
a  slender  tube  of  mica  which  is  then  slipped  into  an  outer  tube  of 
fire-resisting  porcelain  closed  at  one  end.    The  free  ends  of  the 
wire  are  brought  out  of  the  other  end  and  arranged  for  attachment 
to  a  resistance-measuring  instrument  which  may  be  at  some  dis- 
tance.   The  porcelain  tube  is  then  inserted  into  an  opening  in  the 
walls  of  the  furnace  or  dipped  into  the  molten  metal  whose  tem- 
perature is  to  be  determined.     When  the  coil  has  attained  the 
temperature  of  the  surrounding  medium,  the  resistance  of  the  wire 
is  measured  by  means  to  be  described  later  (Chap.  26)  and  the 
corresponding  temperature  is  given  by  reference  to  a  table  or  is 
sometimes  read  directly  from  a  scale  which  is  a  component  part 
of  the  apparatus. 

291.  The  Ohm  Defined  in  Terms  of  a  Column  of  Mercury. — 

The  comparisons  in  Par.  284  are  only  crude  approximations  and 
can  hardly  be  made  anything  more,  for  the  resistance  of  iron  and 
of  copper  varies  greatly  with  even  slight  traces  of  impurities  and 
with  the  temper  and  annealing.  Mercury  is  a  metal  which  by 
simple  distillation  and  washing  is  readily  obtained  in  a  high  state 
of  purity;  it  is  also  free  from  the  troubles  of  tempering  and  anneal- 
ing and  finally  its  resistance  is  nearly  sixty  times  greater  than  that 
of  copper.  The  apparent  disadvantage  of  not  being  able,  on  ac- 
count of  its  liquid  state,  to  obtain  it  in  wires  is  easily  overcome 
by  pouring  it  into  glass  tubes  of  the  required  size,  and  electric 
connection  with  it  is  made  by  simply  dipping  into  it  the  conducting 
wires.  The  International  Congress  of  Electricians  in  Chicago  in 
1893  (Pars.  212,  232)  defined  and  recommended  that  there  be 
adopted  "as  a  unit  of  resistance,  the  International  Ohm  .  .  .  repre- 
sented by  the  resistance  offered  to  an  unvarying  electric  current 
by  a  column  of  mercury  at  a  temperature  of  melting  ice,  14.4521 
grammes  in  mass,  of  a  constant  cross-sectional  area  and  of  the 
length  of  106.3  centimeters."  This  corresponds  to  a  cross-section 


218  ELEMENTS  OF  ELECTRICITY. 

of  one  square  millimeter  but  the  weight  of  the  mercury  is  given 
instead  of  the  diameter  of  the  tube  since,  of  the  two,  the  weight 
is  the  more  easily  and  accurately  measured. 

292.  Resistance  and  Conductance. — The  terms  resistance  and 
conductance  are  reciprocals.    The  less  the  resistance  of  a  conductor, 
the  greater  its  conductance;  the  greater  its  resistance,  the  less  its 
conductance.     The  unit  of  resistance  is  the  ohm.     There  is  no 
need  for  a  unit  of  conductance  yet  it  has  been  given  a  name,  the 
mho  (the  word  ohm  backwards).     A  body  whose  resistance  is 
three  ohms  has  a  conductance  of  one-third  mho. 

There  is  no  conductor  devoid  of  resistance;  so  also  there  is  no 
absolute  non-conductor.  Substances  may  be  arranged  in  order  of 
their  relative  conductance  or,  as  it  is  frequently  called,  their 
conductivity,  this  being  the  reciprocal  of  specific  resistance,  also 
called  resistivity.  Silver  is  the  best  conductor  and  copper  comes 
next.  Conductivity  is  expressed  in  percentage,  that  of  annealed 
copper  being  taken  as  100  since  copper  and  not  silver  is  the  stand- 
ard material  for  electric  wiring.  The  following  table  gives  the 
conductivity  of  the  commoner  metals  as  determined  by  Fleming 
and  others. 

Metal  Conductivity 

Silver,  pure 108.60 

Copper,  annealed a.  .  .100.00 

Gold : 97.80 

Aluminum 63.00 

Zinc 27.72 

Brass 22.15 

Iron,  wrought,  average 15 . 00 

Steel 11.60 

Lead 7.82 

German  Silver 5.32 

Mercury 1 . 69 

293.  Resistance   of   Conductors   in    Parallel. — If   an   electric 
circuit  splits  into  two  or  more  portions  which  again  unite,  it  Is 
called  a  divided  circuit.    Such  a  circuit  of  three  branches  is  repre- 
sented in  Fig.  120.    The  three  branches  are  said  to  be  in  parallel. 
A  turnout  which  enables  cars  travelling  at  different  speeds,  or  in 
opposite  directions  on  a  single  track,  to  pass  each  other  is  some- 
times called  a  shunt.    From  analogy,  any  branch  of  a  divided 


VOLTAIC  ELECTRICITY.  219 

circuit   may  be   called   a  shunt   for  the  remaining  branch  or 
branches. 

It  frequently  becomes  necessary  to  determine  the  resistance  of 
a  divided  circuit,  that  is,  the  joint  resistance  of  two  or  more  con- 
ductors in  parallel.  Suppose  we  have  in  parallel  two  wires,  one  of 

A 


Fig.  120. 

ten  ohms  and  the  other  of  one  ohm  resistance;  what  is  their  joint 
resistance?  The  tendency  for  a  beginner  is  to  say  the  average  of 
the  two,  but  reflection  will  show  that  the  two  wires  side  by  side 
are  equivalent  to  a  single  wire  of  greater  cross-section  and  hence  of 
less  resistance  than  either.  In  other  words,  the  joint  resistance 
of  any  number  of  resistances  in  parallel  is  always  less  than  that 
of  the  least. 

Joint  resistance  may  be  determined  as  follows:  If  A,  B  and  C 
be  the  resistances  of  the  branches  in  Fig.  120,  their  conductance 

is  -j>  ^  and  ~.  Their  joint  conductance  is  the  sum  of  the 
separate  conductances  or 

i   '  I  4_  I  =  AB  +  AC  +  BC 

A  +  B  "*"  C  ABC 

Their  joint  resistance  is  the  reciprocal  of  this  or 

p_  ABC 

~  AB  +  AC  +  BC 

and  in  general  the 

joint  resistance  of  any  number  of  resistances  in  parallel  is  the 
reciprocal  of  the  sum  of  the  reciprocals  of  the  separate  resistances. 
If  there  be  but  two  resistances,  the  formula  becomes 


or  the  joint  resistance  is 
the  product  of  the  two  divided  by  their  sum. 
Should  A,  B  and  C  be  equal,  the  expression  becomes 

R  =  - 

and  in  general  the  joint 


220  ELEMENTS  OF  ELECTRICITY. 

resistance  of  any  number  of  equal  resistances  in  parallel  is  equal  to 
that  of  a  single  resistance  divided  by  the  number  in  parallel. 

294.  Internal    Resistance   of   Cells. — In   the   employment   of 
voltaic  cells  as  a  source  of  electrical  energy,  the  question  of  their 
resistance  is  of  great  importance.    In  Par.  288  we  saw  that  while 
the  specific  resistance  of  copper  is  about  1.6  microhms  (million ths 
of  an  ohm),  that  of  the  usual  electrolytes  runs  from  1  to  30  ohms, 
that  is,  the  resistance  of  the  electrolyte  is  on  an  average  10,000,000 
times  greater  than  that  of  the  copper.    This  resistance,  spoken  of 
as  the  internal  resistance  of  the  cell,  follows  the  same  laws  as  other 
resistances  (Par.  285).    With  a  given  electrolyte,  we  may  reduce 
the  internal  resistance  of  a  cell  in  two  ways.    First,  by  bringing  the 
plates  of  the  cell  closer  together  we  may  shorten  the  path  which 
the  current  has  to  follow.    Second,  by  increasing  the  area  of  the 
plates  we  increase  the  number  of  available  paths  for  the  current, 
or  increase  the  cross-section  of  the  total  path.    A  thin  sheet  of 
copper  parallel  and  close  to  the  zinc  plate  offers  far  less  resistance 
than  the  same  mass  of  copper  in  a  more  compact  form.    As  the 
zinc  and  copper  plates  are  flattened  out  and  increased  in  size  the 
glass  cell  must  keep  pace,  but  as  it  gets  larger  it  increases  rapidly 
in  cost.    Reflection  will  show  that  two  cells  in  parallel  are  elec- 
trically equal  to  a  single  cell  with  plates  twice  as  large.    Therefore, 
the  usual  method  of  increasing  the  cross-sectional  area  of  a 
battery  is  to  join  cells  in  parallel. 

295.  Wire  Tables. — As  the  practical  electrician  has  to  deal 
largely  with  wires,  it  is  important  that  he  should  possess  infor- 
mation as  to  the  different  sizes,  their  dimension,  weight,  resistance, 
etc.    Such  data  is  embodied  in  wire  tables  which  are  issued  by  the 
wire  manufacturers  and  are  also  found  in  the  various  electrical 
hand-books.    The  sizes  of  wire  are  designated  by  numbers  corre- 
sponding to  certain  wire  gauges.    It  is  unfortunate  that  there  are 
in  existence  four  or  five  of  these  gauges  and  that  their  numbers 
do  not  correspond  nor  do  their  sizes  of  wire  vary  in  accordance 
with  any  fixed  rule.    In  this  country  the  gauge  in  most  common 
use  is  the  American  wire  gauge  of  the  Brown  and  Sharpe  Company. 
The  Birmingham  wire  gauge  is  also  in  use.    The  No.  1  wire  on  the 
Brown  and  Sharpe  gauge  is  very  nearly  .3  of  an  inch  in  diameter, 
and  the  smallest  wire,  or  No.  40,  is  about  .003  of  an  inch.    There 
are  four  sizes  larger  than  No.  1  and  they  are  designated  single  0, 


VOLTAIC  ELECTRICITY. 


221 


double  0,  treble  0,  etc.  The  No.  10  wire  on  the  B.  &  S.  gauge  is 
just  about  .1  of  an  inch  in  diameter  and  if  of  copper  its  resistance 
is  about  one  ohm  per  1000  feet.  As  a  rule  of  thumb,  by  subtracting 
three  from  the  gauge  number  of  any  wire  we  get  the  number  of 
the  wire  whose  cross-sectional  area  is  twice  as  great.  The  cross- 
sectional  area  of  No.  7  is  twice  that  of  No.  10. 


COPPER  WIRE  TABLE,  BROWN  AND  SHARPE  GAUGE. 
Resistance  at  20°  C. 


Size  of 
wire 

Diameter, 
inches 

Ohma  per 
foot 

Feet  per 
ohm 

Pounds  per 
foot 

0000 

0.460 

0.00004893 

20,440 

0.6405 

000 

0.4096 

0.00006170 

16,210 

0.5080 

00 

0.3648 

0.00007780 

12,850 

0.4028 

0 

0.3249 

0.00009811 

10,190 

0.3195 

1 

0.2893 

0.0001237 

8,083 

0.2533 

2 

0.2576 

0.0001560 

6,410 

0.2009 

3 

0.2294 

0.0001967 

5,084 

0.1593 

4 

0.2043 

0.0002480 

4,031 

0.1264 

5 

0.1819 

0.0003128 

3,197 

0.1002 

6 

0.1620 

0.0003944 

2,535 

0.07946 

7 

0.1443 

0.0004973 

2,011 

0.06302 

8 

0.1285 

0.0006271 

1,595 

0.04998 

9 

0.1144 

0.0007908 

1,265 

0.03963 

10 

0.1019 

0.0009972 

1,003 

0.03143 

11 

0.09074 

0.001257 

795.3 

0.02493 

12 

0.08081 

0.001586 

630.7 

0.01977 

13 

0.07196 

0.001999 

500.1 

0.01568 

14 

0.06408 

0.002521 

396.6 

0.01243 

15 

0.05707 

0.003179 

314.5 

0.009858 

16 

0.05082 

0.004009 

249.4 

0.007818 

17 

0.04526 

0.005055 

197.8 

0.006200 

18 

0.04030 

0.006374 

156.9 

0.004917 

19 

0.03589 

0.008038 

124.4 

0.003899 

20 

0.03196 

0.01014 

98.66 

0.003092 

21 

0.02846 

0.01278 

78.24 

0.002452 

22 

0.02535 

0.01612 

62.05 

0.001945 

23 

0.02257 

0.02032 

49.21 

0.001542 

24 

0.02010 

0.02563 

39.02 

0.001223 

25 

0.01790 

0.03231 

30.95 

0.0009699 

26 

0.01594 

0.04075 

24.54 

0.0007692 

27 

0.01420 

0.05138 

19.46 

0.0006100 

28 

0.01264 

0.06479 

15.43 

0.0004837 

29 

0.01126 

0.08170 

12.24 

0.0003836 

30 

0.01003 

0.1030 

9.71 

0.0003042 

222  ELEMENTS  OF  ELECTRICITY. 

296.  Circular  Measure  of  Wires. — Owing  to  the  errors  likely 
to  occur  from  lack  of  agreement  in  the  sizes  of  the  various  wire 
gauges,  it  is  becoming  more  and  more  the  custom  among  elec- 
tricians to  designate  wires  by  their  diameters  expressed  in  thous- 
andths of  an  inch  or  mils,  indeed,  by  recent  orders  of  the  War 
Department  this  has  been  made  mandatory  for  our  army.  If  we 
compare  the  area  of  cross-section  of  a  wire  whose  diameter  is  one 
mil  with  that  of  one  whose  diameter  is  n  mils  we  see,  since  the 
areas  of  circles  are  to  each  other  as  the  squares  of  their  diameters, 
that  the  cross-section  of  the  larger  wire  is  n2  times  greater  than 
that  of  the  smaller.  Because  of  this  very  simple  relation,  the  area 
of  cross-section  of  a  wire  of  one  mil  diameter  is  taken  as  the  unit 
of  area  and  called  a  circular  mil  To  find  the  area  in  circular  mils 
of  the  cross-section  of  any  other  wire  we  simply  square  its  diameter 
expressed  in  thousandths  of  an  inch.  This  method  of  comparison 
is  very  much  simpler  than  expressing  the  cross-sections  in  square 
inches.  A  piece  of  wire  one  foot  long  and  one  mil  in  diameter  is 
called  a  mil  foot.  The  resistance  of  a  mil  foot  of  annealed  copper 
is  9.59  ohms  at  32°  F  and  10.505  ohms  at  75°  F.  With  this  data 
we  may,  by  applying  the  law  given  in  Par.  287,  determine  the 
resistance  of  a  copper  wire  of  any  size  and  length. 


-\ 


VOLTAIC  ELECTRICITY.  223 


CHAPTER  25. 

OHM'S  LAW. 

297.  Ohm's  Law. — As  a  result  of  his  investigations,  Ohm 
announced  in  1827  the  law  which  bears  his  name  and  which  is  to 
the  effect  that  in  any  electric  circuit  the  current  varies  directly 
as  the  electro-motive  force  and  inversely  as  the  resistance  of  the 
circuit.  Expressed  in  symbols  this  becomes 

I-E 
~  R 

in  which,  if  E  be  the  E.  M.  F.  in 
volts  and  R  the  resistance  in  ohms,  I  is  the  current  in  amperes. 

In  its  determination  Ohm  employed  the  rather  crude  appliances 
which  he  extemporized  for  the  purpose  (Par.  284).  Since  his  time^ 
the  delicacy  and  accuracy  of  electrical  apparatus  have  been 
immensely  increased,  yet  the  most  careful  and  refined  observations 
serve  merely  to  afford  stronger  confirmation  of  his  conclusions. 

The  importance  of  this  law  can  not  be  over-estimated.  In  the 
study  and  application  of  electricity  it  is  fundamental  and  in  one 
form  or  another  it  is  met  at  every  turn.  On  account  of  its  very 
simplicity  there  is  sometimes  a  failure  to  recognize  that  it  is 
unique,  and  occasionally  it  is  spoken  of  as  "self  evident."  Such 
is  far  from  being  the  case.  There  is  no  material  substance  which 
follows  such  a  law.  Pressure  causes  liquids  and  gases  to  flow 
through  pipes,  yet  if  this  pressure  be  doubled  the  flow  is  by  no 
means  doubled. 

When  applying  the  law  to  a  more  or  less  complex  circuit,  E 
represents  the  total  E.  M.  F.  and  R  the  total  resistance.  Thus  there 
may  be  several  cells  or  batteries  or  electrical  machines  contrib- 
uting to  the  E.  M.  F.,  in  which  case  the  sum  of  the  E.  M.  F.s 
must  be  taken.  Again,  through  error  or  by  design  a  cell  or  battery 
may  be  reversed  so  as  to  oppose  the  remaining  E.  M.  F.  Such 
opposing  E.  M.  F.  is  spoken  of  as  counter  E.  M.  F.  or  back  E.  M.  F. 
Back  E.  M.  F.  is  also  produced  by  polarization  (Par.  198)  and, 
as  we  shall  see  later,  by  the  operation  of  motors  in  the  circuit.  In 


224 


ELEMENTS  OF  ELECTRICITY. 


summing  up  the  total  E.  M.  F.  of  the  circuit,  back  E.  M.  F.  is  to 
be  considered  as  negative.  The  resistance  R  includes  not  only 
the  resistance  of  the  line  but  also  that  of  the  contacts,  joints  and 
connections  and  of  the  electrolyte  and  elements  of  the  cells.  The 
law  can  therefore  be  given 

T      E'  +  E"  +  E'"  +  E""  +  (fee. 
R'  4-  R"  +  E'"  +  R""  +  &c. 

or  the  current 

in  the  circuit  is  equal  to  the  algebraic  sum  of  the  separate 
E.  M.  F.s  divided  by  the  sum  of  the  separate  resistances. 

298.  Drop  of  Potential. — The  three  quantities,  current,  electro- 
motive force  and  resistance  are  bound  together  by  Ohm's  law  so 
that  any  two  being  given,  the  third  may  be  determined.  It  may 
at  first  sight  appear  unnecessary  to  state  such  a  self-evident  truth 
but  it  is  desirable  to  lay  especial  emphasis  upon  the  fact  for,  until 
the  student  has  become  familiar  with  the  law,  the  tendency  is 
rather  to  restrict  its  use  to  the  determination  of  current  only. 

The  law  may  be  put  in  the  form 

E  =  IR 

and  it  is  helpful  to  the 

beginner  if  he  will  accustom  himself  to  interpret  this  as  meaning 
that  E  is  the  electro-motive  force  necessary  to  drive  a  current 
of  strength  /  through  a  resistance  R. 


> 

V          ] 

D"           F" 

r~<~ 

I 
D1 

t                           ^^^ 

1 

\^     i 

1             F       ^                       B 

Fig.  121. 

Suppose  AB  (Fig.  121)  to  represent  a  portion  of  an  electric 
circuit,  the  point  A  being  of  higher  potential  than  B,  and  suppose 
that  by  means  of  one  of  the  instruments  to  be  described  later 
(Chapter  34)  we  measure  the  difference  in  potential  between 
A  and  B.  Lay  off  on  some  convenient  scale  A  A'  proportional 
to  this  difference  of  potential.  If  we  move  along  A  B  to  some 
point  D  and  measure  the  difference  of  potential  between  D  and  B 


VOLTAIC  ELECTRICITY.  225 

we  will  find  it  to  be  less  than  that  at  A,  or  represented  by  DD'~ 
Likewise,  at  F  this  difference  of  potential  is  still  smaller  and  is 
proportional  to  FF',  that  is,  as  we  move  from  A  towards  B  the 
difference  of  potential  between  the  successive  points  and  B 
steadily  grows  less,  or  there  is  a  falling  off  from  the  difference  of 
potential  represented  by  A  A'.  At  D,  for  example,  this  drop  of 
potential  is  D"D'  and  at  F  it  is  F"F'. 

The  drop  of  potential  between  any  two  points  is  always  equal 
to  the  product  of  the  current  into  the  resistance  between  the  points. 
Certain  elementary  applications  of  this  principle  will  be  shown 

in  the  following  paragraphs. 

• 
299.  Ohm's  Law  Applies  to  Any  Portion  of  the  Circuit. — In  Par. 

297  we  saw  that  Ohm's  law  was  applicable  to  the  entire  circuit 
even  though  this  be  made  complex  by  including  heterogeneous 
resistances  and  sources  of  E.  M.  F.  It  also  applies  to  any  portion 
of  a  circuit,  that  is,  the  current  flowing  between  any  two  points 
in  a  circuit  is  equal  to  the  difference  of  potential  between  these 
two  points  divided  by  the  resistance  between  them.  We  have  seen 
(Par.  229)  that  the  current  at  every  cross-section  of  a  circuit  is  the 
same;  if,  therefore,  we  determine  it  at  one  point  we  have  it  for 
any  other  point.  Knowing  the  current,  if  we  have  the  resistance 
between  two  points  we  can,  by  what  we  have  shown  in  the  pre- 
ceding paragraph,  determine  the  difference  of  potential,  or  drop, 
between  the  two  points.  These  principles  enable  us  to  solve  a 
variety  of  problems.  For  example,  let  A  BCD,  Fig.  122,  repre- 
sent part  of  an  electric  circuit.  The  resistance  of  the  portion  AB  is 
12  ohms,  that  of  the  incandescent  lamp  EC  is  220  ohms,  that  of 
CD  is  8  ohms.  The  difference  of  potential  between  A  and  B  is  6 
volts.  What  current  is  flowing  in  the  circuit  and  what  is  the  poten- 
tial of  the  points  A,  B  and  C  if  that  of  D  be  taken  as  zero? 

A         12,  OHMS  B 

-"• * 

.^^         220  OHMS 
8  OHMS 


Fig.  122.' 

V        fi        1 

The  current  between  A  and  ^  =  ^  =  To  =  o  amPere>  which  is 

also  the  current  for  the  rest  of  the  circuit.    The  drop  from  B  to  C  = 


226  ELEMENTS  OF  ELECTRICITY. 


1^  =  ^X220  =  110  volts;  that  from  C  to  D  =  ^X8  =  4  volts.  The 
potential  of  C  is  therefore  4  volts,  that  of  B  is  114,  and  that  of  A 
is  120. 

300.  Division  of  Current  in  Divided  Circuit.—  This  principle  of 
drop  of  potential  furnishes  a  simple  determination  of  the  division 
of  an  electric  current  in  a  divided  circuit. 

I'  R' 


A  j       I" 

R" 

D 

r 

R1" 

Fig.  123. 

Let  Fig.  123  represent  a  divided  circuit  of  three  branches  whose 
resistances  are  respectively  R',  R"  and  R'".  Call  the  correspond- 
ing currents  /',  I"  and  /"'  '.  The  current  in  the  main  branch  upon 
arriving  at  A  divides  into  these  three  portions  which  reunite  at  B. 
The  drop  from  A  to  B  is  the  same  over  each  of  the  three  routes, 
therefore 

I'R'=I"R"=T"R'" 

which  may  be  written 

f  -  f"  •  1'"  —         •          • 

R'  '  R"  '  R"' 

that  is,  the  current 

in  the  branches  of  a  divided  circuit  are  to  each  other  inversely  as  the 
resistances  of  the  respective  branches. 

In  making  an  actual  calculation,  if  the  fractions  in  the  second 
member  of  this  proportion  be  brought  to  a  common  denominator, 
their  numerators  indicate  at  once  the  relation  between  the  several 
currents. 

If  there  be  but  two  branches,  the  above  becomes 

i  -         .    -*- 
R'  '  R 

which  may  be  written 

/'  \l"  =  R"  \R' 

a  somewhat  simple 
form  for  calculations. 

301.  Shunts.  —  In  practical  electricity  it  frequently  becomes 
necessary  to  employ  a  divided  circuit  of  two  branches  which  must 


jt  .  ji 

'     " 


VOLTAIC  ELECTRICITY.  227 

be  so  proportioned  that  the  main  current  divides  between  them 
in  accordance  with  some  desired  ratio.  For  example,  suppose  that 
we  wish  to  measure  a  current  which  is  much  larger  than  can  be 
measured  directly  by  the  instruments  at  our  disposal.  If  we  can 
arrange  a  divided  circuit  so  that  exactly  one-hundredth  of  the 
total  current  flows  through  one  branch,  we  can  measure  this 
small  current  and  always  know  that  the  entire  current  is  one 
hundred  times  greater.  This  division  is  brought  about  by  shunts 
(Par.  293). 

In  Fig.  124  we  desire  to  measure  the  current  flowing  in  AD. 
G  is  our  measuring  instrument  which  with  its  connecting  wires, 
BG  and  GC  has  a  resistance  of  R  ohms.  EC  is  the  shunt.  What 
must  be  the  resistance  of  the  shunt  so  that  one-hundredth  of  the 
total  current  will  flow  through  G  ? 


Fig.  124. 

Call  the  current  through  the  instrument  /;  that  through  BC 
will  be  997.  If  x  be  the  resistance  of  BC,  then,  as  shown  in  the 
preceding  paragraph 

/  X  R  =  997  X  x 

whence  _  R 

~99 

or  the  resistance  of  the  shunt 

must  be  one-ninety-ninth  of  the  resistance  of  G  and  its  connecting 
wires  and  leads.  In  a  similar  manner  we  can  determine  the 
resistance  of  shunts  to  bring  about  division  of  the  total  current  in 
any  desired  ratio.  It  is  to  be  noted  that  these  shunts  are  con- 
structed for  use  with  a  particular  instrument  and  cannot  be  used 
with  another  of  different  resistance. 

302.  Rheostats. — A  consideration  of  Ohm's  law,  I  =  E/R,  will 
show  that  by  varying  R  we  can  vary  the  current  inversely  and 
suggests  that  by  introducing  or  removing  resistance  from  a  cir- 
cuit we  may  regulate  the  current  at. will.  Instruments  for  this 
purpose  are  called  rheostats.  The  principle  of  their  use  will  be 


228  ELEMENTS  OF  ELECTRICITY. 

understood  from  the  diagram  (Fig.  125).  A  series  of  metal  con- 
tacts are  arranged  upon  the  arc  of  a  circle  DE  and  connected 
between  these  contacts  are  resistance  coils.  Pivoted  at  the  center 


B 


t>f  the  arc  is  a  metal  arm  CD  which  can  be  moved  about  over  the 
contacts.  Suppose  the  current  to  come  in  by  A.  As  represented 
in  the  figure,  it  must  now  traverse  all  the  coils  from  D  to  E  before 
it  can  leave  by  B,  and  it  is  therefore  cut  down.  Had  the  arm  CD 
been  still  farther  to  the  left,  the  circuit  would  have  been  broken 
entirely,  R  would  have  been  infinite  and  the  current  zero.  As  the 
arm  is  slid  around  to  E  the  coils  are  successively  cut  out,  the 
resistance  correspondingly  reduced,  and  the  current  correspond- 
ingly increased,  reaching  its  maximum  when  the  arm  reaches  E. 
The  controller  by  which  the  motorman  starts  and  stops  a  trolley 
car  is  similar  in  principle. 

It  will  be  shown  later  that  regulation  of  current  by  rheostat  is 
a  wasteful  method  and  except  for  temporary  purposes,  such  as  for 
starting  and  stopping  motors,  should  not  be  employed. 

303.  KirchoflPs  Laws. — Where  an  electric  circuit  is  composed 
of  interlacing  branches  and  especially  where  there  are  in  it  several 
seats  of  electro-motive  force,  confusion  and  uncertainty  may 
arise  as  to  the  correct  way  of  applying  Ohm's  law  in  the  determina- 
tion of  the  separate  currents  and  pgtentials.  To  obviate  this, 
Kirchoff  has  formulated  a  set  of  rules  which  render  this  applica- 
tion almost  mechanical.  These  are: 

I.  //  several  conductors  meet  at  a  common  point,  the  algebraic  sum 
of  the  currents  in  these  conductors  is  zero. 

This  is  but  a  statement  of  the  fact  that  electricity  does  not 
accumulate  at  a  point  and  that  therefore  as  much  flows  away  as 
flows  to  the  point.  If  currents  flowing  to  the  point  be  considered 
positive,  those  flowing  away  must  be  regarded  as  negative. 

II.  //  two  or  more  conductors  form  a  closed  figure,  or  a  mesh  in  a 
network  of  conductors,  the  sum  of  the  products  of  each  current  of  this 


VOLTAIC  ELECTRICITY. 


229 


mesh  into  the  resistance  through  which  it  passes  is  equal  to  the  algebraic 
sum  of  the  electro-motive  forces  acting  around  this  same  mesh. 

This  is  another  statement  of  the  fact  that  the  total  drop  of 
potential  in  going  around  a  closed  circuit  is  equal  to  the  sum  of 
the  partial  drops.  The  convention  must  be  adopted  that  in  going 
around  a  closed  circuit,  if  the  E.  M.  F.  acting  in  a  clockwise  direc- 
tion be  considered  positive,  that  acting  in  the  opposite  direction 
is  negative. 

304.  Example  of  Application  of  Kirchoff's  Laws. — By  combin- 
ing these  laws  it  is  always  possible  to  obtain  as  many  independent 
equations  as  there  are  unknown  quantities  and  hence  these 
unknown  quantities  may  be  determined.  The  following  concrete 
example  will  make  the  matter  clear.  Fig.  126  represents  a  net- 
work of  conductors  in  two  of  the  branches  of  which  there  are  bat- 
teries E  and  F,  sources  of  E.  M.  F.  The  currents  in  the  separate 


branches  are  designated  ii,  i2,  iz,  etc.,  and  their  assumed  direction 
is  indicated  by  the  arrows.  In  the  final  solution,  a  negative  value 
of  a  current  indicates  that  the  actual  direction  is  opposite  to  that 
assumed.  The  E.  M.  F.  of  the  batteries  and  the  resistances  of  the 
branches  are  indicated  on  the  diagram.  We  are  required  to  deter- 
mine the  currents  in  the  separate  branches. 

From   Kirchoff's   first   law   we   obtain   the   following   "point 
equations"  : 


point  a 
point  6 
point  c 
point  d 


—  ii  —  is  =  0 
-f  i-0  —  i\  =  0 

—  i*  —  is  =  0 
-f  it  —  ib  =  0 


230  ELEMENTS  OF  ELECTRICITY. 

p 

From    the  second    law   we   obtain    the    following    "voltage 
equations": 

mesh  iii&t        5ii  +  2iz  4-  3i4  =  3 
mesh  fciaie        3i3  —  4t6  —  2^  =  0 
mesh  iii&s        4i6  +  4^5  —  3i4  =  —  2 
mesh  w3^5        5ii  -h  3i3  -f-  44  =  3  —  2 


We  now  have  eight  independent  equations  from  which  to  deter- 
mine six  unknown  quantities,  and  the  remainder  of  the  process  is 
but  a  matter  of  combination  and  elimination. 

305.  Lost  Volts  and  Useful  Volts.  —  Should  there  be  connected 
up  to  a  circuit  of  resistance  R  a  cell  whose  E.  M.  F.  is  E  and  in- 
ternal resistance  r,  the  resulting  current  would  be  given  by  the 
expression 


R  +  r 

which  may  be  written 

E  =  IR  +  Ir 

Interpreting  this  as  explained  in  Par.  298,  we  see  that  a  part  of 
the  E.  M.  F.  of  the  cell  is  spent  in  driving  the  current  through  the 
external  resistance  R  and  the  remainder  in  driving  this  current 
through  the  internal  resistance  of  the  cell.  The  volts,  Ir,  con- 
sumed on  the  interior  of  the  cell  are  called  the  lost  volts  and  we 
profit  only  by  those  upon  the  external  circuit,  or  IR,  which  are 
therefore  called  the  available  or  useful  volts.  Since  the  less  the  lost 
volts,  the  more  the  useful  volts,  it  is  of  importance  to  keep  the 
former  at  a  minimum.  Ir  may  be  reduced  in  two  ways;  by  reduc- 
ing the  current  or  by  decreasing  the  internal  resistance.  If  there 
be  no  current,  there  is  of  course  no  wastage.  The  internal  resist- 
ance may  be  reduced  by  selecting  an  electrolyte  of  low  resistance 
(though  usually  choice  is  restricted),  by  bringing  the  plates  closer 
together,  and  by  increasing  the  size  of  the  plates  (Par.  294).  Lost 
volts  have  also  to  be  considered  in  the  operation  of  electrical 
machinery. 

306.  Short  Circuit.  —  The  commonest  source  of  injury  to  elec- 
trical machinery  is  a  short  circuit,  which  may  be  defined  as  the 
removal,  usually  accidental,  of  the  greater  part  of  the  resistance 
from  a  "live"  circuit. 


VOLTAIC  ELECTRICITY.  231 


v 


Suppose  B  (Fig.  127)  to  represent  a  battery  supplying  current 
for  the  incandescent  lamp  L.  The  internal  resistance  of  the  bat- 
tery is  almost  negligible,  the  resistance  of  the  wires  should  be  very 


4. 


Fig.  127. 

small.  Suppose  the  E.  M.  F.  of  the  battery  to  be  111  volts,  the 
resistance  of  the  lamp  to  be  220  ohms  and  that  of  the  battery 
and  wires  to  be  2  ohms.  The  current  is 

1  =  220  +  2  =  2  amPere 

If  by  some  accident  the  wire  should  sag,  as  shown  by  the  dotted 
line,  and  touch  the  lower  wire  at  P,  at  that  instant  the  current 
would  be  short  circuited  through  the  point  P,  the  resistance  of  the 
lamp  and  of  the  wire  beyond  P  being  eliminated.  The  current  is 
now 


I  =  -=—  =  HI  amperes 

or  it  has  suddenly  in- 
creased over  two  hundred  times.  If  the  wires  had  been  designed 
to  carry  only  ten  or  fifteen  amperes  they  will  be  fused,  apparatus 
in  the  circuit  will  be  "burned  out,"  insulation  will  be  charred  and 
possibly  fires  started.  To  avoid  the  injury  resulting  from  such 
accidents,  use  is  made  of  fuses,  pieces  of  soft,  easily-fusible  wire 
inserted  in  the  circuit  which  is  to  be  protected.  If  the  current 
exceeds  that  which  the  fuses  are  intended  to  carry,  they  melt 
before  damage  is  done  to  the  rest  of  the  circuit.  This  same  pro- 
tection is  also  afforded  by  certain  automatic  apparatus  called 
overload  switches  (Par.  414). 

307.  Definitions  Based  Upon  Ohm's  Law. — Since  the  three 
quantities  7,  E  and  R  are  bound  together  by  Ohm's  law,  any  one 
may  be  defined  in  terms  of  the  other  two.  Thus  the  ampere  is 
sometimes  defined  as  the  current  produced  by  an  E.  M.  F.  of  one 
volt  applied  to  a  conductor  whose  resistance  is  one  ohm.  So  also 
the  volt  is  defined  as  that  E.  M.  F.  which  applied  to  a  resistance  of 
one  ohm  will  produce  in  it  a  current  of  one  ampere.  The  ohm  may 


232  ELEMENTS  OF  ELECTRICITY. 

be  similarly  defined  but  such  definition  adds  but  little  to  our 
knowledge. 
Since  Ohm's  law  may  be  written 


and  since  E  and  /  fluctuate 

together  so  that  R  remains  always  constant,  the  resistance  of  a 
conductor  is  defined  by  some  writers  as  the  ratio  of  the  difference 
of  potential  of  the  ends  of  the  conductor  to  the  current  produced 
in  it.  To  define  a  property  as  a  ratio  is  not  altogether  satisfactory. 
It  is  perhaps  better  to  say  that  this  ratio  affords  a  measure  of  the 
resistance. 


VOLTAIC  ELECTRICITY.  233 

CHAPTER  26. 

MEASUREMENT   OF   RESISTANCE. 

308.  Measurement  of  Resistance. — One  of  the  most  important 
classes  of  measurements  with  which  the  electrician  has  to  deal  is 
that  of  resistance.    Logically,  this  subject  should  have  been  taken 
up  in  connection  with  that  of  resistance  in  Chapter  24,  but  the 
methods  employed  could  not  be  clearly  presented  until  after  the 
consideration  of  Ohm's  law  and  the  explanation,  as  given  in  Chap- 
ter 25,  of  the  principles  of  the  drop  of  potential  and  the  division 
of  current  in  a  divided  circuit.    Even  now  we  shall  have  to  antici- 
pate certain  principles  which  can  not  be  fully  developed  until 
later. 

In  these  measurements,  the  methods  to  be  employed  vary  with 
the  amount  and  character  of  the  resistance.  Thus,  very  high  and 
very  low  resistances  are  measured  in  a  different  way  from  those 
covering  a  moderate  range.  Again,  the  measurement  of  the  in- 
ternal resistance  of  cells  and  of  the  resistance  of  electrolytes  must 
be  undertaken  in  an  entirely  different  manner  from  that  of  a 
metallic  conductor.  These  facts  will  be  brought  out  in  the  follow- 
ing pages. 

309.  Drop   of   Potential    Proportional   to    Resistance    Passed 
Over. — If  there  exists  between  AB  (Fig.  128),  two  points  of  a  cir- 


cuit, a  difference  of  potential  E,  there  will  be  a  flow  of  electricity 
from  the  point  of  higher  potential  to  that  of  lower.  The  value  of 
this  current  as  given  by  Ohm's  law  is  I  =  E/R,  whence  E=IR, 
which  last  expression,  as  we  have  already  seen  (Par.  298),  may  be 
interpreted  as  expressing  the  fact  that  E  is  the  electro-motive 
force  required  to  drive  a  current  of  strength  /  through  the  con- 
ductor of  resistance  R. 


234  ELEMENTS  OF  ELECTRICITY. 

To  drive  the  same  current  through  a  resistance  only  one-half  as 
great  requires  only  one-half  as  much  E.  M.  F.,  or,  if  the  resistance 
of  AM  be  one-half  of  the  total  resistance  between  A  and  B,  then 
one-half  of  the  total  E.  M.  F.  will  be  expended  in  driving  the  cur- 
rent from  A  to  M,  and  the  difference  of  potential  between  M  and 
B  is  only  one-half  of  that  between  A  and  B.  In  more  general 
terms,  for  a  constant  current,  the  expenditure  of  E.  M.  F.,  or  the 
drop  of  potential,  is  directly  proportional  to  the  resistance  passed 
over. 

310.  Measurement   of   Resistance    by    Drop    of   Potential. — 

Should  we  have  at  our  disposal  a  known  resistance  and  an  instru- 
ment for  measuring  difference  of  potential  (Chapter  34),  the  fore- 
going affords  us  a  means  of  measuring  the  resistance  between  any 
two  points  in  a  circuit.  For  example,  suppose  that  the  resistance 
R  between  A  and  M,  Fig.  128,  be  known  and  that  we  desire  to 
determine  the  resistance  x  between  M  and  B.  We  have  simply 
to  measure  with  our  instrument  the  drop  E'  between  A  and  M, 
and  the  drop  E"  between  M  and  B.  From  the  preceding  paragraph 

E'  :E"  =  R:x 

E" 
whence  x  =  -^7  R 

This  method  supposes  the  current  to  be  constant  during  the  two 
observations;  the  battery  should  therefore  be  one  of  constant 
E.  M.  F.  and  the  observations  should  be  taken  in  quick  succession 
so  as  to  avoid  change  in  the  current  due  to  the  increase  of  the 
resistance  of  the  circuit  caused  by  the  heating  effect  of  the  current. 

311.  Resistance    Coils. — The   known  resistances  used  as   de- 
scribed in  the  preceding  paragraph  are  usually  in  the  form  of  coils. 
These  resistance  coils,  especially  those  used  as  standards  of  resist- 
ance, are  made  with  great  care  and  accuracy  and  embody  many 
refinements.     They  range  from  .001  of  an  ohm  to  10,000  ohms. 
A  section  of  one  is  shown  in  Fig.  129.    From  the  ebonite  lid  there 
extends  downwards  a  hollow  metal  cylinder  which  has  an  insulat- 
ing covering  of  shellac-coated  silk.  Around  this  cylinder  is  wrapped 
the  coil  proper  which  is  of  silk-insulated  manganin  wire  (Par.  289). 
For  reasons  which  are  explained  later  (Par.  315),  the  wire  is 
doubled  upon  itself  at  its  middle  point  and  the  winding  is  begun 
at  this  loop.    The  ends  of  the  coil  are  attached  to  heavy  copper 


VOLTAIC  ELECTRICITY. 


235 


terminals  bent  downward  as  shown.  The  coil  is  connected  up  in 
the  circuit  by  inserting  these  turned-down  ends  into  mercury  cups 
which  in  turn  are  connected  to  the  lead  wires.  The  whole  is  pro- 


Fig.  129. 

tected  by  a  brass  case  which  is  perforated  by  many  small  openings. 
The  object  of  the  interior  metal  cylinder  is  to  conduct  away  heat 
developed  in  the  wire  and  at  the  same  time  to  afford  a  large  sur- 
face for  radiation.  The  object  of  the  openings  is  to  allow  the 
enclosed  coil  to  cool  off  more  rapidly  and  also  to  permit  the  tem- 
perature to  be  kept  down  by  submerging  the  entire  coil  in  oil. 
The  plug  in  the  center  of  the  lid  is  to  permit  the  insertion  of  a 
thermometer  for  reading  the  temperature  of  the  coil  so  that  the 
proper  correction  for  temperature  may  be  applied. 

312.  Drop  in  Divided  Circuit. — The  usual  way  of  measuring 
ordinary  resistances  is  by  means  of  the  Wheatstone  bridge,  a  piece 
of  apparatus  whose  principle  will  be  understood  from  the  following 
explanation.  Consider  a  divided  circuit  of  two  branches  and  let 
A  (Fig.  130)  be  the  point  of  high  potential.  The  current  at  B 
divides  into  two  parts  inversely  proportional  to  the  resistances  of 
the  two  branches,  i.  e.,  the  greater  part  goes  along  the  branch  of 
least  resistance,  the  lesser  part  along  the  branch  of  greater  resist- 
ance. There  is  a  continuous  drop  of  potential  along  each  branch 
of  the  circuit  from  B  to  D,  in  other  words,  the  drop  of  potential 
over  the  two  branches  is  exactly  the  same.  Suppose  following  the 
right  hand  branch  we  reach  a  point  M  at  which  we  have  passed 
over  one-half  of  the  resistance  in  that  branch;  the  difference  of  po- 
tential between  M  and  D  is  only  one-half  of  that  between  B  and  D. 


236 


ELEMENTS  OF  ELECTRICITY. 


Fig.  130. 


Similarly,  following  the  left  hand  branch  and  reaching  a  point 

N  at  which  we  have  passed  over  one-half  of  the  resistance  in  that 
A  branch,  the  difference  of  potential  between 

I  JV  and  D  is  only  one-half  of  that  between  B 

and  D.  Hence,  the  points  M  and  N  are  at 
the  same  potential.  This  can  be  shown  by 
connecting  between  these  points  a  sensitive 
galvanometer  G.  (Galvanometers  are  de- 
scribed in  Chapter  30.  For  the  present  it  is 
sufficient  for  us  to  know  that  a  galvanometer 
(more  strictly  a  galvanoscope)  is  an  instru- 
ment which  indicates  by  the  movement  of 
its  needle  that  a  current  is  flowing  in  the 
circuit  of  which  it  forms  a  part,  and  by  the 
direction  of  the  motion  of  the  needle  indi- 
cates the  direction  of  the  current.)  Should 
there  be  a  difference  of  potential  between  M 
and  N,  a  current  would  be  produced  and 
would  be  revealed  by  a  deflection  of  the  gal- 
vanometer needle,  but  the  needle  will  be  found  to  remain  at  rest. 
The  foregoing  illustration  is  based  on  the  supposition  that  the 

resistance  of  BM  and  of  B  N  are  each  one-half  of  the  resistance  of 

the  respective  branches,  but  the  prin- 
ciple is  equally  true  for  I/nth,  that  is, 

if  the  resistance  of  BM  be  I /nth  of 

that  of  the  right  hand  branch  and  the 

resistance  of  B  N  be  I/nth  of  that  of 

the  left  hand  branch,  the  points  M  and 

N  will  be  at  the  same  potential  and 

there  will  be  no  flow  of  current  between 

them  if  they  be  connected  through  a 

galvanometer. 

313.  Principle   of   the   Wheatstone 

Bridge. — Let  us  now  consider  a  divided 

circuit  of   two   branches    (Fig.  131), 

each  branch  subdivided  into  two  parts 

as  shown,  and  suppose  that  in  the  left 

hand  branch  we  know  the  resistance 


Fig.  131. 


of  A  and  of  R  and  further  can  vary  that  of  R  at  pleasure,  and 
that  in  the  right  hand  branch  we  know  the  resistance  of  the 


VOLTAIC  ELECTRICITY  237 

portion  B  but  do  not  know  that  of  the  remainder  X  and  wish  to 
determine  it.  Of  the  total  resistance  of  the  right  hand  branch, 
X  is  some  definite  fraction,  say  I /nth.  Since  R  may  be  varied  at 
pleasure,  it  can  be  adjusted  so  that  it  is  1/wth  of  the  total  resist- 
ance in  the  left  hand  branch.  When  such  a  state  of  affairs  is 
reached,  the  points  M  and  N  will,  from  what  has  been  shown 
above,  be  at  the  same  potential  and  the  galvanometer  connected 
between  M  and  N  will  reveal  no  current.  The  system  is  now 
said  to  be  "balanced." 

Since  X  is  I/rath  of  the  total  resistance  in  the  right  hand  branch, 
B  is  n  —  1/wths,  and  since  R  has  been  made  1/wth  of  that  in  the 
left  hand  branch,  A  is  n  —  1/wths. 

Hence  A  :  B  :  :  R  :  X 

Whence  X 

or,  when  the  system  has  been 

brought  to  a  balance,  the  resistance  in  X  is  equal  to  the  product  of 
the  resistances  in  the  adjacent  arms  divided  by  that  of  the  opposite  arm. 

314.  A  Second  Demonstration. — The  same  thing  can  be  readily 
shown  by  applying  the  principle  of  drop  directly.  Call  the  current 
in  the  left  hand  branch  I',  that  in  the  right  hand  branch  I",  and 
the  resistance  in  the  four  arms  A,  B,  R,  and  X,  respectively.  The 
drop  from  S  to  N  is  equal  to  the  current  times  the  resistance  or 
FA;  that  from  S  to  M  is  equal  to  I"B.  But  M  and  N  being  at 
the  same  potential  these  drops  are  equal.  Similarly,  the  drop 
from  N  to  T,  or  I'R,  is  equal  to  the  drop  from  M  to  T,  or  I"X. 

We  then  have  the  two  equations, 

(I)  FA  =  T'E 

(II)  I'R  =I"X 

Dividing  (II)  by  (I)  and  striking  out  common  factors 

R      X 
A=B 

Whence  as  above 

BR 


The  foregoing  is  the  principle  upon  which  the  Wheatstone 
bridge  is  constructed. 


238 


ELEMENT^  OF  ELECTRICITY. 


"DT>  T> 

The  expression  X  =  — r-  can  be  written  X  =  -j  R,  whence  it  is 

seen  that  if  B  and  A  be  so  selected  that  B/A  is  some  multiple  or 
submultiple  of  ten,  calculations  will  be  simplified  since  all  that 
will  then  be  necessary  will  be  to  point  off  decimal  places  or  add 
zeros  to  the  value  of  the  known  resistance  R. 

315.  Arrangement  of  Resistances. — In  the  actual  apparatus 
the  resistance  in  the  arms  A,  B,  and  R  is  usually  varied  by  re- 
moving or  changing  the  position  of  certain  plugs.  For  example, 


Fig.  132. 

the  arm  A,  a  portion  of  which  is  represented  in  Fig.  132,  consists 
of  a  heavy  brass  bar  DE  secured  to  the  ebonite  plate  FF  and  cut 
entirely  through  at  regular  intervals  by  tapering  openings  into 
which  fit  the  corresponding  ebonite-handled  brass  plugs  A,  B,  C. 
The  separate  sections  into  which  the  bar  is  divided  are  connected 
beneath  the  plate  FF  by  the  resistance  coils  G,  H,  K.  These  are 
wound  as  described  in  Par.  311  so  as  to  avoid  self-induction.  For 
the  present  we  may  explain  this  by  stating  that  when  a  circuit 
through  a  coil  of  wire  is  completed  there  is  produced  through 
induction  an  opposing  E.  M.  F.  which  causes  the  current  to  lag 
and  prevents  it  from  rising  to  its  full  strength  at  once.  When  a 
coil  is  made  by  winding  it  from  a  loop  at  its  middle  point,  each 
turn  of  the  coil  carrying  a  current  is  paralleled  by  an  equal  turn 
in  which  the  current  flows  in  the  opposite  direction  and  the 
inductive  effects  of  the  two  turns  exactly  neutralize  each  other. 
These  coils  have  a  resistance  of  1  ohm,  10  ohms,  100  ohms,  etc., 


VOLTAIC  ELECTRICITY. 


239 


and  therefore  bear  to  each  other  the  ratio  of  1  :  10  :  100,  etc. 
With  the  plugs  in  position  the  current  passes  from  DtoE  through 
the  bar  and  coils,  the  combined  resistance  of  which  is  so  small  as 
to  be  negligible.  With  the  plug  B  removed,  the  current  must 
follow  the  path  D  M  H  N  E,  that  is,  the  resistance  of  the  coil 
H  has  been  introduced  into  the  circuit. 

In  the  arm  R  the  arrangement  is  similar  but  there  is  a  much 
greater  number  of  coils  whose  resistances  are  in  ohms  1,  2,  3,  4, 
10,  20,  30,  40,  100, 200,  300, 400,  1000, 2000,  3000,  4000,  etc.,  thus 
enabling  any  combination  from  1  to  11110  to  be  obtained.  This 
arm  is  usually  called  the  "rheostat"  and  is  consequently  desig- 
nated in  diagrams  by  letter  JR. 

316.  Evolution  in  Form. — The  theory  of  the  Wheatstone 
bridge  is  best  explained  as  above  from  a  diagrammatic  diamond- 


(5) 


shaped  figure  as  in  (1),  Fig.  133.  The  commercial  form  of  this 
apparatus  bears  no  superficial  resemblance  to  the  figure  but  has 
been  evolved  directly  from  it  as  the  following  will  show. 

1st  step.  The  galvanometer  need  not  be  placed  in  the  diamond 
but  may  be  connected  outside  as  shown  in  (2). 

2d  step.  A  and  B  need  not  make  an  angle  with  each  other 
but  may  be  flattened  down  as  shown  in  (3). 

3d  step.  R  being  the  arm  which  carries  the  greatest  number 
of  resistance  coils  should,  relatively  to  A  and  B,  be  elongated  as 
shown  in  (4). 

4th  step.  Finally,  for  the  sake  of  compactness,  the  arm  R 
may  be  folded  back  upon  itself  as  shown  in  (5). 

Other  minor  changes  consist  in  the  arrangement  of  the  terminals 
to  facilitate  connections,  and  in  the  insertion  in  the  battery  and 


240 


ELEMENTS  OF  ELECTRICITY. 


galvanometer  circuits  of  keys  permanently  attached  to  the  instru- 
ment. Sometimes  a  galvanometer  is  included  in  the  case.  The 
final  result  is  an  instrument  of  which  Fig.  134  shows  a  form  made 
by  the  Leeds  &  Northrup  Co. 


Fig.  134. 


The  various  circuits  between  the  keys  and  other  parts  of  the 
bridge  are  inside  the  case  but  are  usually  indicated  by  white  lines 
marked  on  the  cover. 

317.  Connections  for  a  Measurement. — Whatever  be  the  form 
of  the  bridge  it  is  well-  to  bear  in  mind  the  following: — first,  the 
current  enters  (or  leaves)  at  the  junction  of  A  and  B  and  leaves 
(or  enters)  at  the  junction  of  R  and  X',  second,  the  galvanometer 
is  connected  between  the  junction  of  A  and  R  and  that  of  B  and  X. 
(It  should  however  be  observed  that  it  may  readily  be  shown  that 
the  battery  and  the  galvanometer  may  be  interchanged,   the 
resistance  of  their  respective  leads  altered  at  will,  and  the  E.  M.  F. 
of  the  battery  varied,  all  this  without  affecting  the  balance.) 
Finally,  in  the  factor  by  which  R  is  to  be  multiplied,  the  resistance 
of  B,  the  arm  connected  to  X,  is  the  numerator  and  that  of  A, 
the  arm  opposite  X,  is  the  denominator. 

318.  Operation  of  Measurement. — To  measure  the  resistance, 
say  of  a  wire  X,  the  apparatus  is  brushed  free  from  dust,  and 
plugs  brightened,  being  especially  careful  to  remove  all  grease 


VOLTAIC  ELECTRICITY. 


241 


or  oil  so  as  to  insure  perfect  contacts.  Connections  are  then  made 
as  shown  in  Fig.  135.  A  plug  is  removed  from  coil  of  the  same 
resistance  in  both  A  and  B,  their  ratio  therefore  being  unity. 
Various  plugs  are  then  removed  from  R  until  with  both  battery 


Fig.  135. 

and  galvanometer  keys  closed  the  apparatus  is  as  nearly  balanced 
as  possible.  At  this  point  the  sum  of  the  unplugged  resistances 
in  -R  is  as  near  the  unknown  resistance  X  as  it  is  possible  to  get 
with  the  ratio  of  unity  in  B/A. 

319.  Bracketing. — The  plugs  in  R  are  not  removed  at  hap- 
hazard but  preferably  the  resistance  should  be  arrived  at  by  a 
system  of  "bracketing."  For  example,  the  first  plug  to  be  removed 
should  be  selected  so  that  the  resistance  thrown  in  is  certainly 
greater  or  less  than  the  one  to  be  measured.  Suppose  it  to  be  less. 
The  battery  key  K  is  closed  and  then  the  galvanometer  key  H. 
Suppose  the  galvanometer  needle  to  be  deflected  to  the  left. 
Replace  the  plug  and  remove  a  second  one  so  as  to  throw  in  a 
resistance  certainly  greater  than  that  to  be  measured.  Upon 
closing  the  keys,  if  the  needle  is  now  deflected  to  the  right  the 
unknown  resistance  lies  between  the  two.  Replace  the  plug  and 
remove  a  third  which  will  throw  in  a  resistance  as  near  half  way 
of  the  interval  between  the  first  two  as  possible.  If  upon  closing 
the  keys  the  needle  is  deflected  to  the  left,  the  third  resistance  is 
too  small,  if  to  the  right  it  is  too  great.  Proceed  in  this  way 
keeping  the  unknown  resistance  between  limits  and  halving  the 
interval  at  each  successive  attempt. 


'242  ELEMENTS  OF  ELECTRICITY. 

With  a  little  experience  the  bracketing  can  be  materially 
shortened  by  observing  the  amount  of  swing  produced  in  the 
needle  by  the  trial  resistances.  This  decreases  rapidly  as  the 
correct  resistance  is  approached  and  indicates  which  of  two  is  the 
nearer. 

320.  Order  of  Closing  Keys. — The  order  in  which  the  battery 
and  galvanometer  keys  are  closed  is  not  a  matter  of  indifference. 
It  is  essential  that  the  battery  key  be  closed  first.    For  consider 
Fig.  135.    The  coils  in  R  are  wound  so  as  to  avoid  self-induction 
but  this  object  may  not  be  completely  attained  and  with  a  number 
of  coils  unplugged  the  inductance  may  not  be  negligible.    Again, 
if  the  resistance  X  be  that  of  a  coil,  especially  if  it  be  wrapped 
around  an  iron  core,  its  self-induction  will  be  large.    Finally,  if  X 
be  a  cable  it  may  have  considerable  capacity  as  a  condenser.    In 
any  of  these  cases,  when  the  battery  key  K  is  closed  the  current 
will  not  rise  at  once  to  its  full  strength  in  the  branch  affected. 
Suppose  the  bridge  to  be  balanced  accurately  and  the  galvanom- 
eter key  closed  first;  when  K  is  closed  the  current  in  one  branch 
or  the  other  not  rising  at  once  to  its  full  strength,  M  and  N  will 
be  momentarily  at  different  potentials  and  there  will  be  an  in- 
stantaneous rush  of  current  through  G  causing  a  deflection  of  the 
needle  and  incorrectly  indicating  a  lack  of  balance.    On  the  other 
hand,  if  K  be  closed  first  there  will  still  be  this  retardation  but  its 
effect  will  disappear  in  a  fraction  of  a  second,  M  and  N  will  reach 
the  same  potential  and  when  H  is  closed  there  will  be  no  deflection 
of  the  galvanometer  needle. 

There  may  be  used  'ajspecial  key  which  by  making  successive 
contacts  as  it  is  pressed  down  will  insure  the  proper  sequence  of 
closing. 

To  avoid  violent  swings  of  the  needle,  the  galvanometer  key  at 
first  should  be  given  a  mere  tap. 

321.  Proper  Ratio  to  Use. — The  first  determination  gives  the 
resistance  of  X  to  the  nearest  unit  or  ohm.    If  it  be  desired  to 
measure  it  to  the  first,  second,  or  third  place  of  decimals,  the  plugs 
in  A  and  B  must  be  so  adjusted  that  the  ratio  B/A  is  .1,  .01,  or 
.001  and  the  corresponding  decimal  places  are  pointed  off  in  the 
final  reading  of  R.    If  the  resistance  to  be  measured  be  large,  the 
ratio  B/A  must  be  10,  or  100,  or  1000. 

It  will  be  noted  that  some  of  the  ratios  can  be  obtained  by  several 


VOLTAIC  ELECTRICITY. 


243 


different  combinations,  thus  }£,  %%%,  !#££>  all  giye  the  ratio  unity. 
It  can  be  shown  that  other  things  being  equal,  the  greatest  sensi- 
bility is  obtained  when  the  resistances  in  the  four  arms  of  the 
bridge  are  as  nearly  equal  as  possible.  For  example,  if  the  resist- 
ance to  be  measured  is  about  100  ohms  and  this  is  to  be  measured 
to  the  nearest  unit,  the  ratio  should  be  {%%,  or  if  to  the  nearest 
tenth  then  TVA- 

The  instrumental  sensibility  depends  directly  upon  the  sensi- 
tiveness of  the  galvanometer,  or  its  ability  to  indicate  very  minute 
currents  when  the  bridge  is  nearly  balanced. 

322.  Bridge  with  Reversible  Ratios. — There  is  sometimes  used, 
instead  of  the  bridge  described  above,  a  variation  by  which  a  coil 
is  saved  in  each  of  the  arms  A  and  B,  making  six  instead  of  eight, 
and  yet  the  same  ratios  are  preserved. 


(2) 


Fig.  136. 


Its  arrangement  is  shown  in  (2)  in  Fig.  136  and  is  as  if  the  arms 
A  and  B  of  (1)  had  been  separated  at  S  and  each  rotated  outward 
from  the  center.  These  outer  ends  (2)  are  then  connected  by  a 
heavy  wire  with  S  which  must  now  be  regarded  as  the  junction 
of  A  and  B  and,  according  to  Par.  317,  is  the  point  at  which  the 
battery  current  enters.  The  inner  ends  of  A  and  B  are  connected 
to  the  R  and  the  X  arms  by  movable  plugs.  With  the  plugs  in 
the  positions  shown  by  the  small  circles  in  (2),  A  is  connected  to 
R  and  B  to  X.  If  these  plugs  be  shifted  to  the  positions  marked 
by  the  crosses,  A  becomes  connected  to  X  and  B  to  R,  in  other 
words  (see  Par.  317),  A  and  B  interchange. 


244 


ELEMENTS  OF  ELECTRICITY. 


The  A  arm  contains  the  coils  1,  10,  100,  the  B  arm  10,  100, 
1000.  The  smallest  B/A  ratio  obtainable  with  the  plugs  in  the 
first  position  is  TW  or  .1.  If  it  be  desired  to  use  a  smaller  one,  shift 
the  two  plugs,  A  becomes  B  and  B  becomes  A,  and  the  ratios 
T£«y  and  joVo  become  available. 

323.  The  Dial  Bridge. — In  the  bridges  described  above,  resist- 
ances are  thrown  in  the  rheostat  by  removing  plugs.  There  are 
other  forms,  such  as  the  dial  bridge  and  the  decade  bridge,  in 
which  resistances  are  introduced  by  inserting  plugs.  The  connec- 
tions of  a  dial  bridge  are  shown  diagrammatically  in  Fig.  137. 


coooooioooocp 


Fig.  137. 

The  A  and  B  arms  are  like  those  of  the  ordinary  bridge  but  the 
rheostat  is  composed  of  dials,  usually  four,  which  are  marked 
units,  tens,  hundreds,  and  thousands,  respectively.  Each  dial 
consists  of  a  heavy  center  piece  of  brass  surrounded  by  ten  key- 
stone shaped  pieces,  these  being  numbered  0,  1,  2,  etc.,  to  9. 
Between  the  successive  keystone  pieces,  except  numbers  9  and  0, 
are  resistance  coils,  those  at  each  dial  being  all  of  the  same 
resistance.  Thus,  at  the  unit  dial  each  coil  has  a  resistance  of  one 
ohm;  at  the  ten  dial  each  has  a  resistance  of  ten  ohms,  and  so  on. 
The  current  entering  by  A  goes  to  the  center  of  the  first  dial,  then 
through  the  plug  to  the  corresponding  keystone  piece,  thence 
through  the  coils  in  series  to  the  0  keystone  and  thence  to  the 
second  dial,  etc.  The  diagram  represents  a  resistance  plugged  in 
of  5135  ohms. 

This  form  is  more  expensive  than  the  first  but  has  a  number  of 
advantages,  among  them,  the  smaller  number  of  plugs  to  be 
handled  and  consequent  smaller  number  of  contacts  (four  as  com- 
pared to  fifteen  or  more)  and  the  much  less  danger  of  error  in 
reading  off  resistances. 


VOLTAIC  ELECTRICITY. 


245 


324.  Resistances   that   may   be   Measured    by   Bridge. — The 

bridge  is  not  suited  to  the  measurement  of  very  high  or  of  very  low 
resistances.  Theory  requires  that  with  the  plugs  inserted  the 
resistances  in  the  arms  should  be  zero  while,  as  a  matter  of  fact, 
they  have  a  resistance  which  may  affect  the  fourth  place  of  deci- 
mals. The  resistance  in  the  contacts  of  the  plugs  themselves  may 
affect  the  third  place.  Therefore,  in  measuring  very  small  resist- 
ances these  neglected  resistances  may  cause  a  considerable  error, 
and  in  the  case  of  a  very  large  resistance  any  error  in  the  balance 
is  multiplied  a  hundred  or  a  thousandfold  by  applying  the  ratio 
B/A.  In  general,  the  measurements  should  lie  between  .01  and 
100,000  ohms. 

325.  The  Slide  Wire  Bridge.— A  simplified  form  of  bridge,  used 
especially  in  the  measurement  of  low  resistances,  is  the  so-called 
slide  wire  bridge.    This  consists  (Fig.  138)  of  a  wire  WW  of  uniform 


Fig.  138. 


cross-section  stretched  between  heavy  copper  terminals  and  above 
a  graduated  scale.  Since  this  scale  is  usually  a  meter  subdivided 
into  millimeters,  the  instrument  is  often  called  a  "meter  bridge." 
Connections  are  made  as  shown  in  the  figure,  R  being  a  standard 
resistance  coil  (Par.  311)  whose  resistance  is  preferably  as  near  as 
possible  to  that  of  X,  the  resistance  to  be  measured.  The  terminal 
P  of  the  galvanometer  is  slid  backwards  and  forwards  along  the 
wire  WW  until  balance  is  attained,  at  which  point,  if  A  and  B 
be  the  resistances  of  the  corresponding  portions  of  the  wire,  we 
have,  as  in  any  other  bridge,  X  =  BR/A.  Since  the  wire  is  of 
uniform  cross-section,  the  resistance  of  the  portions  is  directly 
proportional  to  their  lengths,  hence  in  the  above  expression  the 
lengths  of  A  and  B,  which  may  be  read  directly  from  the  printed 
scale,  can  be  and  are  used  instead  of  the  actual  resistances,  which 
last  need  not  be  known  at  all. 


246 


ELEMENTS  OF  ELECTRICITY. 


326.  Measurement  of  High  Resistance.— The  principle  of  the 
measurement  of  high  resistance  is  simple.  We  measure  accurately 
the  current  driven  through  the  resistance  by  a  known  E.  M.  F., 
whence,  by  Ohm's  law,  the  resistance  is  obtained  at  once.  For 
example,  to  measure  the  resistance  of  the  rubber  insulation  of  a 
reel  of  submarine  cable,  the  entire  cable,  except  the  two  free  ends, 
is  submerged  in  a  tank  of  water  (Fig.  139).  To  one  of  fcne  ends  of 


Fig.  139. 


the  cable  core  is  attached  a  terminal  of  a  battery.  The  other 
terminal  is  connected  to  G,  a  very  delicate  current-measuring 
instrument  (a  reflecting  galvanometer,  Par.  378),  and  the  circuit 
is  completed  by  a  wire  extending  from  G  and  dipping  into  the  water 
in  the  tank.  The  E.  M.  F.  of  the  battery  is  measured  by  the 
instrument  V,  and  the  resulting  current  by  G,  whence  R  follows 
from  Ohm's  law.  Reflection  will  show  that  should  the  total 
length  of  the  cable  be  n  yards,  the  average  resistance  per  yard  is 
n  times  the  total  resistance.  In  actually  carrying  out  this  measure- 
ment, many  refinements  and  precautions  are  observed,  not 
necessary  to  mention  here. 

327.  Measurement  of  Resistance  of  Electrolytes. — The  re- 
sistance of  an  electrolyte  can  not  be  measured  by  the  means 
described  above.  We  have  seen  (Par.  215)  that  the  passage  of  a 
current  through  an  electrolyte  produces  chemical  decomposition; 
the  current  used  in  balancing  a  bridge  would  therefore  bring  about 
this  electrolysis.  If  gas  be  released  at  either  anode  or  cathode,  the 
resistance  which  we  are  trying  to  measure  would  be  very  greatly 
increased.  Also  the  products  of  electrolysis  will  still  set  up  a  back 
E.M.F.  which  by  cutting  down  the  current  through  the  electrolyte 
would  lessen  the  drop  in  the  corresponding  branch  and  render  value- 
less observations  based  on  movements  of  the  galvanometer  needle. 


VOLTAIC  ELECTRICITY.  247 

We  may,  however,  make  these  measurements  by  employing  a 
rapidly  alternating  current,  that  is,  a  current  which  many  times 
a  second  reverses  its  direction  of  flow.  In  this  case,  a  galvanometer 
can  not  be  used  to  indicate  a  balance  but  in  its  stead  a  telephone 
receiver  is  employed,  taking  the  place  of  G  in  Fig.  138.  So  long  as 
an  alternating  current  flows  through  the  receiver  a  buzzing  sound 
is  produced,  but  when  the  bridge  is  balanced  the  sound  dies  out. 
Explanation  of  these  facts  will  be  given  later. 

328.  Measurement  of  Internal  Resistance  of  Cells. — In  meas- 
uring the  internal  resistance  of  a  cell  the  same  difficulties  are 
encountered  as  in  the  case  of  electrolytes  and  in  addition  the  cur- 
rent produced  by  the  cell  itself  prevents  the  use  of  the  bridge. 
There  are,  however,  several  methods  by  which  this  internal 
resistance  may  be  measured.  The  simplest  is  by  using  the  instru- 
ments for  measuring  E.  M.  F.  and  current,  which  instruments 
will  be  described  in  Chapter  34.  We  first  measure  the  E.  M.  F. 
of  the  cell  when  no  current  is  flowing.  We  then  cause  a  moderate 
current  to  flow  from  the  cell,  measure  this  current  and  the  external 
or  useful  volts  (Par.  305).  The  difference  between  the  E.  M.  F. 
of  the  cell  and  the  useful  volts  is  the  lost  volts  or  Ir,  and  knowing 
I  we  determine  r. 


248  ELEMENTS  OF  ELECTRICITY. 

CHAPTER  27. 
THE   POTENTIOMETER. 

329.  Measurement  of  Electro -Motive  Force  of  Cells.— The 

simplest  and  usual  way  of  measuring  the  electro-motive  force  of 
a  cell  is  by  means  of  a  voltmeter,  an  instrument  described  in  Chap- 
ter 34.  It  will  be  shown,  however,  that  in  order  to  obtain  a  read- 
ing from  the  voltmeter,  there  must  be  a  flow  of  current  through 
the  instrument.  It  is  true  that  this  current  is  so  small  that  for 
all  ordinary  cases  it  is  entirely  negligible,  but  if  there  be  a  current 
there  will  also  be  lost  volts  (Par.  305)  and  since  a  voltmeter  reads 
only  the  useful  volts,  its  indications  are  always  some  slight 
amount  less  than  the  true  E.  M.  F.  Therefore,  to  obtain  strictly 
accurate  results,  the  E.  M.  F.  of  a  cell  should  be  measured  when 
no  current  is  flowing.  This  may  be  done  with  an  electrometer, 
as  explained  in  Chapter  11,  but  preferably  by  a  potentiometer,  an 
instrument  which  we  shall  now  describe. 

330.  Preliminary  Arrangement  of  a   Potentiometer. — Let  us 
suppose  that  we  start  with  one  or  two  cells  giving  us  ajxmstant 

D 


Fig.  140. 

E.  M.  F.  of  about  two  volts,  seven  or  eight  feet  of  rather  thin  wire 
of  uniform  cross-section,  and  a  graduated  paper  scale.  Provided 
the  scale  be  graduated  uniformly,  the  unit  is  immaterial,  but  a 
millimeter  scale  running  up  to  2000  is  very  convenient.  We  will 
tack  the  paper  scale  upon  a  board  AB  (Fig.  140),  and  stretch  the 
wire  above  it.  To  the  end  A  of  the  wire  we  connect  the  negative 
terminal  of  our  cell  C;  the  other  terminal  makes  sliding  contact 
at  P. 


VOLTAIC  ELECTRICITY.  249 

If  the  E.  M.  F.  of  the  cell  be  two  volts,  the  difference  of  potential 
between  P  and  A  before  P  is  touched  to  the  wire  will  be  two  volts 
and  after  contact  is  made  it  will  still  be  aboy^two  volts.  If  it  were 
exactly  two  volts  when  P  is  at  the  2000  division  on  the  scale, 
there  would  be  a  drop  of  two  volts  from  P  to  A  and  each  division 
of  the  scale  would  correspond  to  a  drop  of  one-thousandth  of  a 
volt.  If  P  be  slid  in  towards  A,  these  two  volts  will  be  spread 
over  a  shorter  length  of  the  wire  and  each  division  on  the  scale 
would  correspond  to  a  drop  of  more  than  one-thousandth  of  a  volt. 
On  the  other  hand,  if  P  be  slid  out  from  A,  the  scale  divisions  can 
be  made  to  correspond  to  less  than  one-thousandth  of  a  volt, 
therefore,  by  sliding  P  backwards  and  forwards  we  can  vary  the 
drop  over  the  scale  and  at  one  particular  point  this  drop  will  be 
exactly  one-thousandth  of  a  volt  per  millimeter.  This  point  is 
located  as  follows: 

331.  Calibration  of  Potentiometer. — To  the  same  end  A  of 
our  stretched  wire  we  connect  through  a  galvanometer  G  the 
negative  terminal  of  a  standard  cell  S.    If  this  be  a  Clark's  cell 
whose  E.  M.  F.  is  1.434  volts  (Par.  212),  we  connect  its  positive 
terminal  to  the  wire  at  M,  a  point  1434  millimeters  from  A.    If 
M  be  at  a  higher  potential  than  1.434  volts  a  current  will  flow 
from  M  to  D,  while  if  it  be  at  a  lower  potential  a  current  will  flow 
from  D  to  M.     In  either  case  this  flow  will  be  indicated  by  a 
deflection  of  the  needle  of  the  galvanometer  G.    If  there  be  a  flow, 
we  slide  the  contact  P  backwards  or  forwards  until  a  point  is 
found  where  G  indicates  no  current  and  we  then  know  that  the 
potential  of  M  is  the  same  as  that  of  D,  that  is,  1.434  volts,  and 
that  consequently  each  division  of  the  scale  corresponds  to  a  drop 
of  one-thousandth  of  a  volt.     The  contact  P  is  left  at  this  point. 
The  instrument  is  now  in  adjustment  so  that  the  printed  figures 
on  its  scale  read  thousandths  of  a  volt,  in  other  words,  it  has  been 
calibrated. 

332.  Measurement    with    Potentiometer. — To    measure    the 
E.  M.  F.  of  a  cell  X,  its  negative  terminal  is  connected  through 
the  galvanometer  H  with  A  and  its  positive  terminal  is  con- 
nected to  a  contact  T  which  is  moved  back  and  forth  along  the 
wire  until   H  indicates  no  current.     Suppose  this  point  to  be 
the  925th  millimeter  from  A,  then  the  E.  M.  F.  of  X  is  .925 
volt. 


250  ELEMENTS  OF  ELECTRICITY. 

Instead  of  using  a  second  galvanometer  H,  the  negative  ter- 
minal of  X  could  have  been  attached  to  G,  that  is,  S  and  X  can 
use  G  in  common. 

333.  Forms  of  Potentiometer. — As  in  the  case  of  the  Wheat- 
stone  bridge,  the  actual  instrument  bears  no  resemblance  at  all 
to  the  diagrammatic  representation  in  Fig.  140.  For  example, 
for  the  sake  of  compactness  the  long  wire  is  wound  in  a  helical 
coil  around  an  ebonite  cylinder,  etc.,  etc.  There  are  numerous 
forms  of  potentiometers  but  the  principle  of  all  is  the  same,  that 
is,  they  measure  an  unknown  E.  M.  F.  by  balancing  against  it  an 
equal  and  opposite  E.  M.  F.  which  latter  is  known. 


VOLTAIC  ELECTRICITY. 


251 


CHAPTER  28. 

GROUPING   OF  CELLS  IN  BATTERIES. 

334.  Grouping  of  Cells. — The  cells  composing  a  battery  may 
be  connected  up  in  several  ways.    If  they  are  connected  one  after 
the  other  they  are  said  to  be  in  series.    If  all  of  the  positive  poles 
are  connected  to  one  common  wire  and  all  of  the  negative  poles  to 
another,  they  are  said  to  be  in  parallel.    If  they  are  divided  into 
groups,  the  cells  in  each  group  being  connected  in  series  and  these 
separate  groups  being  then  connected  in  parallel,  the  battery  is 
said  to  be  grouped  in  multiple,  or  better,  so  many  in  parallel  and 
so  many  in  series.    For  example,  if  we  have  ten  cells  we  might 
group  them  all  in  series,  or  all  in  parallel,  or  two  abreast  and  five 
deep,  that  is,  two  in  parallel  and  five  in  series,  or  finally,  five 
abreast  and  two  deep,  that  is,  five  in  parallel  and  two  in  series. 
Each  of  these  arrangements  is  quite  proper  under  certain  condi- 
tions but  it  will  be  shown  in  the  following  paragraphs  that  it  is 
not  a  matter  of  indifference  which  shall  be  employed. 

335.  Cells  in  Series.— In  Par.  192  we  saw  that  in  a  voltaic  cell 
the  copper  or  positive  pole  is  at  a  higher  potential  than  the  zinc 
or  negative  pole.    Suppose  that  we  have  a  number  of  simple  cells, 
each  of  an  E.  M.  F.  of  one  volt,  and  that  we  should  arrange  them 


Fig.  141. 

in  series,  the  copper  plate  of  each,  as  shown  in  Fig.  141,  being 
connected  to  the  zinc  plate  of  the  adjoining  one.  The  copper 
plate  of  A  and  the  zinc  plate  of  B  being  connected  are  at  a  com- 


252 


ELEMENTS  OF  ELECTRICITY. 


mon  potential,  therefore  the  zinc  plate  of  B  is  one  volt  higher  than 
that  of  A.  The  copper  plate  of  B  being  one  volt  higher  than  its 
zinc  plate  is  consequently  two  volts  higher  than  the  zinc  plate  of  A. 
Similarly,  the  copper  plate  of  C  is  three  volts  higher  than  the  zinc 
plate  of  A,  and  in  general  the  total  E.  M.  F.  of  a  number  of  similar 
cells  connected  in  series  is  equal  to  the  E.  M.  F.  of  one  cell  multi- 
plied by  the  number  in  series.  This  principle  applies  even  though 
the  circuit  includes  cells  of  different  kinds,  electrical  machines, 
etc.,  and  the  most  general  statement  is  that  in  any  electric  circuit 
containing  several  sources  of  E.  M.  F.  in  series  the  total  E.  M.  F. 
is  the  sum  of  the  separate  E.  M.  F.s. 

336.  Cells  in  Parallel.— Fig.  142  represents  three  cells  in 
parallel.  The  three  positive  poles  being  brought  together  at  a 
common  point  A  are  all  at  the  same  potential,  that  is,  one  volt 
higher  than  the  three  negative  poles  which  are  brought  together 


Cu 


at  B.  This  combination  therefore  has  no  greater  E.  M.  F.  than 
has  a  single  cell  and  it  is  in  fact,  as  we  have  already  seen  (Par. 
294),  equivalent  to  a  single  cell  whose  copper  and  zinc  plates  are 
three  times  as  large  as  those  of  the  original  cells. 

337.  Comparison  of  Series  and  Parallel  Groupings.  —  We  may 

by  a  concrete  example  best  illustrate  the  different  effect  of  the 
two  kinds  of  groupings.  Suppose  that  we  have  a  number  of  cells, 
each  of  an  E.  M.  F.  of  2  volts  and  an  internal  resistance  of  .25  ohm. 
From  a  single  cell  in  a  circuit  of  negligible  external  resistance  the 
current  obtainable  is 


O25 


=  8 


VOLTAIC  ELECTRICITY.  253 

With  two  in  series,  the  E.  M.  F.  is  twice  as  great  (Par.  335), 
but  also  the  resistance  is  twice  as  great  (Par.  286),  therefore  the 
current  is  the  same,  and  so  on  for  any  number,  that  is,  with  a  cir- 
cuit of  negligible  external  resistance  the  effect  of  grouping  cells 
in  series  is  to  increase  the  voltage  but  not  the  current.  Should, 
however,  the  external  resistance  be  great,  a  different  state  of 
affairs  results.  For  example,  let  R  =  100  ohms  (the  resistance  of 
about  6  miles  of  iron  telegraph  wire),  then  for  one  cell 


100  +  .25 
and  for  two  cells 

1  =  100  +  .50 

The  difference  in  these  denominators  being  negligible,  we  see  that 
in  this  second  case  we  have  doubled  the  current. 

If,  starting  again  with  negligible  external  resistance,  we  arrange 
two  of  these  cells  in  parallel,  the  E.  M.  F.  is  no  greater  than  for 
one  cell  (Par.  336)  but  the  resistances  of  the  two  cells  being  in 
parallel,  the  total  resistance  is  only  one-half  that  of  one  cell  (Par. 
293),  hence  the  current  is  doubled.  For  three  cells  it  is  trebled, 
and  so  on,  that  is,  with  negligible  external  resistance,  the  effect 
of  grouping  cells  in  parallel  is  to  increase  the  current  but  not  the 
voltage. 

With  a  large  external  resistance,  the  grouping  of  cells  in  parallel, 
since  it  does  not  increase  the  E.  M.  F.  nor  change  the  total  resist- 
ance to  any  significant  extent,  does  not  alter  the  current. 

We  may  sum  up  by  saying  that  with  a  large  external  resistance 
we  increase  the  current  by  grouping  the  cells  in  series;  with  a 
small  external  resistance,  we  increase  it  by  grouping  them  in 
parallel. 

338.  Analogy  Between  Voltaic  Cells  and  Pumps. — Difference 
of  potential  has  been  compared  to  difference  of  water  level  (Par. 
70).  Since  a  difference  of  potential  is  produced  in  a  cell,  we  may 
continue  the  comparison  by  drawing  an  analogy  between  a  cell 
and  a  pump.  In  Fig.  143  the  pumps  A  and  B  are  analogous  to 
two  cells  in  parallel;  the  two  lift  the  water  no  higher  than  a  single 
pump  but  they  lift  twice  the  quantity.  The  pumps  C,  D  and  E 


254 


ELEMENTS  OF  ELECTRICITY. 


are  analogous  to  cells  in  series;  they  lift  no  more  water  than  a 
single  pump  but  they  raise  it  three  times  as  high. 


Fig.  143. 


339.  Parallel -Series  Grouping.— Suppose  we  have  N  cells, 
each  of  an  E.  M.  F.  of  e  volts  and  an  internal  resistance  of  r  ohms, 
and  suppose  that  they  are  arranged  (Fig.  144)  s  in  series  and  p  in 


Fig.  144. 

parallel  in  a  circuit  of  external  resistance  R.  The  resulting  E.  M, 
F.  is  equal  to  the  E.  M.  F.  of  one  cell  multiplied  by  the  number  in 
series  (Par.  335)  or  se.  The  resistance  of  one  of  the  series  is  rs, 
but  since  there  are  p  rows  in  parallel,  the  total  internal  resistance 

*  "p" 
The  current  produced  by  this  arrangement  is 

/=    -^- 


340.  Maximum   Current. — The  question  may  arise,  given  N 
cells,  how  should  they  be  grouped  to  obtain  the  maximum  current? 


VOLTAIC  ELECTRICITY.  255 

The  expression  for  the  current  is  given  in  the  preceding  paragraph 
and,  since  N  =  sp,  can  be  written 

T  -       Ne 
NR 

s 

If  this  be  differentiated  and  the  first  differential  coefficient  be 
placed  equal  to  zero,  the  resulting  values  of  s  will  correspond  to 
maximum  or  minimum  values  of  /.  This  differentiation  is  tedi- 
ous. However,  since  Ne  is  a  positive  constant,  /  will  be  a  maxi- 
mum when h  rs,  the  denominator  of  the  expression,  is  a 

s 

minimum. 

Place  x  =  —  -f  rs  =  NRs~l  +  rs 

s 

Differentiating 


Placing  this  equal  to  zero,  we  have 

NR      ,                     A  /NR 
s2  = ,  whence  s  =  d=  y 

which  is  the  value 

sought.  This  will  in  general  only  approximate  to  the  desired 
arrangement  since  the  mathematical  supposition  is  that  s  and  p 
are  continuous  variables,  while  actually  they  are  both  discon- 
tinuous or  positive  whole  numbers.  For  example,  if  N  be  10, 
the  only  possible  values  of  s  are  1,  2,  5  and  10,  yet  the  actual 
solution  will  generally  produce  some  mixed  number.  In  such  a 
case  we  should  make  the  calculation  of  the  current  from  the  two 
groupings  which  come  nearest  to  the  one  indicated  by  the  solution 
and  select  accordingly. 

If  in  the  above  equation  of  condition  for  maximum  current 

S*=NR 
r 

we  substitute  for  N  its  value 
sp,  we  get  _  SpR 

~T 

whence  R=  r- 


256 


ELEMENTS  OF  ELECTRICITY. 


But   (Par.  339)   R  is  the  external  resistance  and  r-  is  the 

internal  resistance,  whence  we  arrive  at  the  important  conclusion 
that  the  current  is  a  maximum  when  the  battery  is  so  grouped  that 
the  internal  and  the  external  resistances  are  equal. 

We  saw  (Par.  305)  that  the  useful  volts  of  a  cell  or  battery  are 
given  by  IR,  the  lost  volts  by  Ir.  Since  in  the  case  of  maximum 
current  R  =r,  the  lost  volts  amount  to  one-half  of  the  total  E.  M.  F. 

341.  In  Multiple  Arrangements  Equal  E.  M.  F.  is  Required 
of  Groups  in  Series. — In  a  parallel-series  arrangement  the  series 
groups  must  all  have  the  same  E.  M.  F.  This  requires  that  where 
the  cells  are  all  of  one  kind  there  should  be  the  same  number  in 
each  series  group.  The  arrangement  shown  in  Fig.  145  is  not 


Fig.  145. 

permissible.  The  battery  should  be  quiescent  when  the  key  K 
is  open  but  the  three  cells  now  constitute  a  closed  circuit  in  which 
the  E.  M.  F.  of  the  two  upper  cells  acting  in  a  clockwise  direction 
is  not  counterbalancedyby  the  opposing  E.  M.  F.  of  the  single 
cell.  If  the  E.  M.  F.  of  each  cell  be  e  and  its  resistance  r,  there 
will  flow  through  the  single  cell  a  reverse  current  whose  strength 
e 


s      = 


3? 


The  elements  of  the  two  upper  cells  will  therefore 


consume  away  and  the  zinc  plate  of  the  single  cell  will  have  copper 
deposited  upon  it  which  will  cause  local  action.  With  K  closed, 
the  loss  is  not  so-  great  and  it  will  diminish  as  the  external  resist- 
ance decreases,  but  even  in  this  case  the  elements  of  the  single 
cell  will  consume  away  much  more  rapidly  than  those  of  the  two 
in  series. 

342.  Diagrams  of  Parallel-Series  Grouping. — A  parallel-series 
grouping  represented  as  in  Fig.  144  doubtless  aids  the  beginner, 
but  in  actual  practice  cells  are  seldom  arranged  in  this  geometrical 
order.  Especially  is  this  the  case  with  storage  batteries  in  which 


VOLTAIC  ELECTRICITY. 


257 


the  cells  are  very  heavy  and  are  placed  in  rows  on  shelves  or 
benches.  Reflection  will  show  that  after  all  it  is  not  necessary  to 
move  the  cells  themselves  but  rather  to  shift  the  connecting 
wires.  Thus  in  Fig.  146  eight  cells  are  represented  in  four  different 


el 


1 1 1 1 1 


K  fl'l'l'lfl'l'l'l1 


Fig.  146. 

groupings,  the  cells  themselves  not  being  disturbed.  In  A  they 
are  all  in  series,  in  B  all  in  parallel,  in  C  four  in  series  and  two  in 
parallel,  and  in  D  two  in  series  and  four  in  parallel. 

343.  Cost  of  Power  from  Primary  Cells. — For  the  small  and 
irregular  currents  required  in  telegraphy  and  in  operating  tele- 
phones, call  bells,  annunciators,  alarms,  etc.,  a  battery  of  primary 
cells  is  the  most  suitable  and  economical  source  of  electrical 
energy,  but  where  the  current  is  required  to  furnish  appreciable 
mechanical  power  through  suitable  machines,  the  cost  is  pro- 
hibitive. The  chemicals  consumed  in  the  cell  correspond  to  the 
fuel  consumed  in  the  boiler  of  a  steam  engine,  and  while  one 
pound  of  carbon  burned  in  air  evolves  enough  heat  to  raise  8080 
pounds  of  water  1°  C,  in  round  numbers  four  pounds  of  zinc  must 
combine  with  six  pounds  of  sulphuric  acid  to  produce  the  same 
amount  of  heat.  With  modern  machines  electrical  energy  may 
be  produced  as  cheaply  as  one  cent  per  horse-power  per  hour  but 
the  same  energy  supplied  from  primary  cells  costs  from  30  to 
50  times  as  much.  Where  many  telephones  or  telegraph  lines 
are  operated  from  a  central  station  it  is  now  the  practice  to  use 
storage  batteries  instead  of  the  batteries  of  Daniell  or  gravity 
cells  formerly  employed. 


ELECTRO-MAGNETICS.  259 


PART  IV. 
ELECTRO-MAGNETICS. 


CHAPTER  29. 

MAGNETIC  FIELD  ABOUT  A   WIRE  CARRYING 
A  CURRENT. 

344.  Oerstedt's  Discovery. — In  1819,  in  the  course  of  a  lecture 
on  electricity,   Oerstedt,  Professor  of  Physics  at  Copenhagen, 
observed  that  when  a  wire  carrying  a  current  was  brought  near  a 
magnetic  needle  a  deflection  of  the  needle  was  produced.     He 
recognized  at  once  the  importance  of  this  discovery  as  demon- 
strating what  up  to  that  time  had  been  merely, a  conjecture,  that 
is,  that  there  existed  some  connection  between  electricity  and 
magnetism.    He  set  to  work  immediately  to  investigate  the  matter 
and  soon  discovered  not  only  that  an  electric  current  produced  a 
deflection  of  a  magnetic  needle  near  it  but  that  the  direction  of 
this  deflection  depended  both  upon  the  direction  in  which  the 
current  was  flowing  and  upon  the  position  of  the  conductor  with 
reference  to  the  needle.     His  results  were  announced  in  1820. 
The  news  reached  the  French  electrician  Ampere  on  September  11 
and  was  received  by  him  with  eagerness.    Within  one  week  there- 
after he  had  repeated  Oerstedt's  experiments  and  had  added  to 
the  latter's  discoveries;  had  confirmed  by  specially  devised  experi- 
ments and  had  presented  in  a  paper  to  the  Academy  a  complete 
theory  of  the  new  science  of  electro-dynamics  (Par.  360) . 

345.  Right  Hand  Rule  for  Deflection  of  Needle. — It  is  helpful 
to  the  electrician,  whether  he  be  an  advanced  student  or  only  a 
beginner,  to  have  some  easy  rule  for  determining,  or  some  mechan- 
ical way  of  remembering,  in  which  direction  certain  phenomena 
take  place.    Thus  Ampere  gave  the  rule  of  the  "swimming  man" 
by  which,  the  relative  positions  of  the  conductor  and  of  the  needle 
and  the  direction  of  the  current  being  given,  the  direction  in 


260 


ELEMENTS  OF  ELECTRICITY. 


which  the  north  end  of  the  needle  would  move  could  be  predicted. 
Other  rules  have  been  given  by  subsequent  writers.  Of  these, 
the  following  is  thought  to  be  the  most  useful,  both  because  of 
its  simplicity,  it  being  a  true  "rule  of  thumb,"  and  because,  as  will 
be  shown  later,  of  its  applicability  to  a  number  of  varied  con- 
ditions. It  should  be  committed  to  memory. 

Place  the  palm  of  the  right  hand  upon  the  wire,  the  extended 
fingers  pointing  in  the  direction  of  the  flow  of  the  current,  the  palm 
turned  towards  the  needle;  the  extended  thumb  will  indicate  the 
direction  in  which  the  north  pole  of  the  needle  will  move. 

Fig.  147  represents  the  application  of  this  rule.  The  current 
flowing  in  the  wire  in  the  direction  indicated  by  the  arrow  will 


Fig.  147. 


cause  the  north  pole  of  the  needle  to  move  out  in  the  direction  in 
which  the  thumb  is  pointing. 

If  the  wire  be  below,  in  order  that  the  palm  should  be  turned 
towards  the  needle,  the  hand  must  be  held  back  down,  in  which 
case  the  thumb  will  point  away  from  the  observer  and  this  is  the 
direction  in  which  the  north  pole  will  actually  move.  In  fact,  the 
rule  is  perfectly  general  and  applies  if  the  wire  be  vertical  and 
in  front  of  either  pole  or  if  it  be  to  either  side  of  the  needle,  only 
in  this  last  case  the  needle  must  be  capable  of  movement  in  a 
vertical  plane. 

346.  Magnetic  Field  About  a  Wire  Carrying  a  Current. — In 

Pars.  143  and  144  it  was  shown  that  a  needle  in  a  magnetic  field 
tends  to  turn  so  as  to  place  its  longer  axis  and  its  own  lines  of 
force  parallel  to  the  lines  of  force  of  the  field.  The  needle  in 
Oerstedt's  experiment  turns  for  the  same  reason,  that  is,  the  cur- 
rent flowing  through  the  wire  establishes  about  this  wire  a  mag- 
netic field  with  which  the  needle  tends  to  coincide  in  direction. 


ELECTRO-MAGNETICS. 


261 


This  field  may  be  studied  in  a  similar  manner  to  the  other 
magnetic  fields  already  described.  If  a  vertical  wire,  a  portion 
of  an  electric  circuit,  be  passed  through  a  hole  in  the  center  of  a 
horizontal  sheet  of  cardboard 
or  of  glass  which  has  been 
sprinkled  with  iron  filings  (Fig. 
148)  and  if  the  circuit  be  then 
closed  and  the  horizontal  sheet 
be  tapped  while  the  current  is 
flowing,  the  filings  will  be  seen 
to  gather  and  form  in  more  or 
less  distinct  circles  around  the 
wire  as  a  center.  The  lines  of 
force  of  the  field  are  circles, 
and  it  was  shown  first  by 


Fig.  148. 


Ampere  that  these  circles  lie 
in  planes  perpendicular  to  the 
wire.  In  Oerstedt's  experiment  as  described  in  Par.  344,  the  needle 
can  never  place  itself  at  right  angles  to  the  wire,  tor  the  controlling 
force,  the  horizontal  component  of  the  earth's  magnetism,  is 
always  effective.  However,  if  a  perfectly  balanced  needle  be 
mounted  so  that  its  axis  of  rotation  is  parallel  to  the  earth's  field, 
then  this  field  has  no  influence  upon  its  rotation  and  if  Oerstedt's 
experiment  be  now  performed,  the  needle  will  always  set  itself 
at  right  angles  to  the  wire. 


u 

Fig.  149. 

347.  Direction  of  Field. — The  experiment  with  the  iron  filings 
shows  the  lines  of  force  of  the  field  to  be  circles  but  does  not 
indicate  their  direction.  This  latter  may  be  determined  as  follows. 


262  ELEMENTS  OF  ELECTRICITY. 

Using  the  same  horizontal  sheet  and  vertical  wire  as  in  the  pre- 
ceding experiment,  distribute  at  equal  distances  apart  on  the 
circumference  of  a  circle  whose  center  lies  on  the  wire  a  number 
of  small  compasses,  A,  B,  C,  D  (Fig.  149).  Before  the  circuit  is 
closed,  these  all  point  in  the  same  direction.  Let  us  assume  that 
this  is  the  direction  indicated  by  the  needle  A.  Suppose  now  the 
circuit  to  be  closed  and  the  current  to  flow  down  the  wire.  The 
needle  at  A  will  not  change  its  position,  C  will  be  entirely  reversed, 
B  will  point  to  the  right  and  D  to  the  left,  that  is,  if  we  look  at 
the  needles  from  above,  they  point  around  the  circle  in  the  direc- 
tion of  the  motion  of  the  hands  of  a  clock.  Had  the  current 
flowed  up,  the  needles  would  all  have  pointed  in  a  counter-clock- 
wise direction  around  the  circle. 

348.  Clock  Rule  for  Direction  of  Field. — The  foregoing  experi- 
ment suggests  another  simple  rule  for  determining  the  direction 
of  the  field  about  a  wire  carrying  a  current. 

Suppose  the  eye  placed  so  as  to  look  along  the  wire  in  the  direction 
in  which  the  current  is  flowing;  the  positive  direction  of  the  field 
about  the  wire  is  the  same  as  the  direction  of  motion  of  the  hands 
of  a  clock. 

Of  course,  if  the  current  is  flowing  towards  the  eye,  the  field  is 
counter-clockwise.  This  rule  should  not  supplant  the  right  hand 
rule  given  in  Par.  345.  Either  one  could  be  used  to  the  exclusion 
of  the  other  but  it  is  better  to  have  both  at  command. 

349.  Wire  Carrying  a  Current  is  not  Itself  a  Magnet. — Although 
surrounded  by  a  magnetic  field,  a  wire  carrying  a  current  is  not 
itself  a  magnet.    If  a  clean  copper  wire  through  which  a  current 
is  flowing  be  dipped  into  iron  filings  and  then  lifted,  the  filings 
will  cluster  around  the  wire  but  will  drop  off  when  the  current  is 
broken.    At  first  sight  this  seems  to  indicate  that  the  wire  has 
become  magnetized  but  it  can  be  shown  that  such  is  not  the  case. 
When  the  wire  is  thrust  into  the  filings  they  become  magnetized, 
since  magnetic  bodies  placed  in  a  magnetic  field  become  magnets 
(Par.  120),  and  if  they  surround  the  wire,  or  if  any  of  them  adhere 
to  it  through  stickiness,  they  cling  together  like  the  links  of  a 
chain  and  really  adhere  to  each  other  instead  of  to  the  wire.    If 
an  elongated  filing  be  placed  at  right  angles  to  the  wire  and  with 
its  ends  lying  upon  one  of  the  circular  lines  of  force  surrounding 
the  wire,  one  of  these  ends  will  be  urged  in  one  direction  around 


ELECTRO-MAGNETICS. 


263 


the  circle,  the  other  end  in  the  opposite  direction;  the  result  is 
that  the  filing  will  move  broadside  towards  the  wire.  There  is, 
however,  no  radial  component  between  a  wire  carrying  a  current 
and  a  magnetic  pole  in  its  field.  In  this  respect  the  field  about  a 
conductor  is  unique.  While  all  other  forces  exerted  between 
bodies  act  along  the  line  joining  the  bodies,  the  force  upon  a  pole 
in  a  field  about  a  wire  acts  at  right  angles  to  the  line  joining  the 
wire  and  the  pole. 

350.  Rotation  of  a  Magnetic  Pole  by  a  Current. — In  Par.  135 
the  positive  direction  of  a  magnetic  field  was  defined  as  that  direc- 
tion in  which  a  free  north  pole  would  move.  Such  a  pole  released 
near  the  north  end  of  a  magnet  would  move  off  along  a  line  of 
force,  curving  around  until  it  came  to  rest  against  the  south  face. 
The  statement  was  made  (Par.  142)  that  a  magnetic  line  of  force 
is  a  closed  curve,  but  the  moving 
pole  can  not  travel  around  a  com- 
plete orbit  for  its  progress  is  arrested 
by  the  material  substance  of  the 
magnet.  In  the  field  about  a  wire 
carrying  a  current  the  case  is  dif- 
ferent. Here  the  lines  of  force  are 
circles,  return  upon  themselves  and 
do  not  necessarily  pass  through  any 
solid  body.  A  pole  released  in  such  a 
field  should  therefore  rotate  as  long 
as  the  field  is  maintained.  Although 
we  can  not  obtain  a  free  pole,  we 
can  approximate  to  the  theoretical 
condition  by  arranging  a  circuit  so 
that  only  one  pole  of  the  magnet 
lies  in  the  field  and  we  can  thus 
produce  mechanical  rotation. 

Fig.     150     represents     diagram- 
niatically  such  an  arrangement.    NS 


Fig.  150. 


is  a  magnet  bent  in  the  center  at  an  angle  and  placed  upon  the 
pivot  P  about  which  it  is  free  to  rotate.  B  is  a  little  cup  of 
mercury  into  which  dips  the  conductor  AB,  thereby  securing 
movable  electric  contact  with  a  minimum  of  friction.  CD  is  an 
annular  cup  of  mercury  surrounding  but  not  touching  the  magnet. 
From  B  a  wire  BD  is  carried  over  and  bent  down  so  as  just  to 


264 


ELEMENTS  OF  ELECTRICITY. 


touch  the  surface  of  the  mercury  at  D  and  to  sweep  along  this 
surface  as  the  magnet  rotates.  DE  is  a  conductor  leading  away 
from  the  annular  cup.  If  the  current  enters  at  A,  it  goes  to  B, 
thence  to  D  and  out  by  E.  It  therefore  passes  by  the  pole  N  but 
not  by  the  pole  S.  According  to  the  rule  given  in  the  preceding 
paragraph,  the  field  about  AB,  viewed  from  A,  is  clockwise.  The 
pole  N  will  therefore  spin 'around  in  the  direction  shown  by  the 
dotted  line.  If  the  current  be  reversed  the  direction  of  rotation 
is  also  reversed;  so  also  if  the  magnet  be  inverted,  the  direction 
of  rotation  is  reversed. 

351.  Rotation  of  a  Current  by  a  Magnetic  Pole. — The  reaction 
between  the  pole  and  the  field  being  mutual,  it  follows  that  if 

the  pole  be  fixed  and  the  conductor  be  free 
to  move,  the  latter  may  be  made  to  rotate 
about  the  former.  This  may  be  shown  by 
the  apparatus  represented  in  Fig.  151.  NS 
is  a  magnet  run  through  a  cork  which  is 
inserted  in  the  lower  end  of  a  short  and 
broad  glass  tube.  The  annular  space  around 
the  projecting  pole  N  is  filled  with  mer- 
cury. A  current  is  led  down  by  the  wire  A, 
through  the  flexible  joint  and  B  into  the 
mercury  cup  and  out  by  C.  While  the 
current  flows  B  is  surrounded  by  lines  of 
force  which  viewed  from  A  are  clockwise. 
If  B  were  stationary  and  N  were  free  to 
move,  N  would  travel  around  B  in  a  clock- 
wise direction,  that  is,  N  would  move  out 
towards  the  observer.  However,  N  being 
fixed,  B  moves  back  from  the  observer  and 
travels  around  AT  in  a  clockwise  direc- 
Fig.  151.  tion. 

352.  Left   Hand   Rule   for    Direction    of   Motion.— The  con- 
ductor described  in  the  preceding  paragraph  is  in  the  field  of 
the  magnet  and  owes  its  motion  to  the  interaction  of  this  field 
with  its  own.     Any  conductor  carrying  a  current  and  placed 
in  a  magnetic  field  will  move  if  it  be '  free  to  do  so.     It  is 
useful  to  have  a  rule  by  which  the  direction  of  this  motion 
can  be  foretold.    The  following  is  such  a  rule.    Place  the  palm 


ELECTRO-MAGNETICS. 


265 


of  the  left  hand  upon  the  wire,  the  extended  fingers  pointing  in 
the  direction  of  the  flow  of  the  current  (Fig.  152)  and  the  palm 
turned  to  receive  the  lines  of  force  of 
the  field;  the  extended  thumb  will  point 
in  the  direction  of  the  motion  of  the  con- 
ductor. 

353.  Intensity  of  Field  About  a 
Straight  Conductor. — A  magnetic  field 
is  known  when  we  have  determined  its 
direction  and  intensity.  We  have 
shown  above  (Par.  347)  how  to  deter- 
mine the  direction  of  the  field  about 
a  conductor  carrying  a  current.  The 
intensity  may  be  measured  as  ex- 
plained in  Pars.  148-150.  In  two  sim- 
ple cases  (which  fortunately  are  the 
ones  most  frequently  encountered),  it 
may  be  calculated.  These  are,  first, 
when  the  conductor  is  straight,  and 
second,  when  it  is  bent  into  the  arc 
of  a  circle. 

In  Fig.  153  let  A  B  represent  a  por- 
tion of  a  straight  wire  of  indefinite  length  carrying  a  current  of 
strength  /.    (The  unit  in  which  /  is  measured  is  for  the  moment 
R  held  in  abeyance;  see  Par.  355.)    Let  m 

represent  a  unit  pole  at  a  distance  r  from 
the  wire.  The  force  exerted  upon  m  will 
measure  the  intensity  of  the  field  at  that 
point  (Par.  136).  Let  A  represent  an 
infinitely  small  section  of  the  wire,  its 
length  being  dy.  It  has  been  shown  by 
Laplace  that  the  force  exerted  upon  a 
magnet  pole  by  an  infinitely  short  element 
of  a  conductor  carrying  a  current  is 
directly  proportional  to  the  strength  of 
the  pole,  to  the  strength  of  the  current, 
to  the  length  of  the  element,  and  to  the 
sine  of  the  angle  which  this  element  makes 
with  the  line  joining  its  center  and  the  pole;  it  is  also  inversely 
proportional  to  the  square  of  the  length  of  this  line.  In  the  case 


Fig.  152. 


y! 


m 


Fig.  153. 


266 


ELEMENTS  OF  ELECTRICITY. 


represented,  the  force  exerted  by  A  upon  the  unit  pole  at  m  is 
therefore 

*  >y»2*  ^     * 

This  expression  integrated  between  proper  limits  will  give  the 
intensity  of  the  field  produced  at  m  by  the  corresponding  lengths 
of  AB. 

r 


From  the  figure  x  = 
also  y 


sin 


tan  a 


,  hence  dy  =  r  ( —  cosec2  a  da) 


Substituting  these  values  in    (I)   and  remembering   that 
cosec  a  =  -r— ,  we  obtain 


sin 


Integrating 


df  =  - .  sin  a  da 
f  =  - .  cos  a  +  a  constant. 


Taking  this  between  the  limits  a  =  0°  and  a  =  180°,  we  have 

/-  — 

or  the  field   at  any  point 

about  an  indefinitely  long  straight  wire  is  directly  proportional  to 
the  current  and  inversely  proportional  to  the  simple  distance  from 
the  wire. 

354.  Field  on  the  Axis  of  a  Circular  Coil.— The  field  produced 
at  a  point  on  the  axis  of  a  circular  coil  may  be  determined  as 

A 


Fig.  154. 

follows:    With  a  current  of  strength  7  flowing  as  indicated  by  the 
arrow  (Fig.  154),  the  infinitely  small  portion  of  the  coil  at  A  exerts 


ELECTRO-MAGNETICS.  267 

upon  a  unit  north  pole  at  P  a  force  in  the  direction  PF  which  is 

— ^-,  dl  being  the  length  of  A.    This  may  be  divided  into  two 
x 

components,  one  PD  =  -^- .  sin  0,    and    the    other    PE.     The 

diametrically  opposite  element  of  the  coil  at  B  likewise  exerts  a 
force  upon  P  which  may  be  divided  into  two  components,  one  in 
the  direction  PD,  the  other  opposite  and  equal  to  PE  and  hence 
counterbalancing  it.  Every  element  of  the  coil  therefore  exerts 
in  the  direction  PD  a  force  upon  P  equal  to 

I.dl 

—  .on* 

The  sum  of  these  elementary  forces  is 

1.2  TTT 

f  =  — 2"  .  sm  6 

Substituting  for  sin  6  its  value  r/x 

f- 

ji>~ 

or,  the  field  at  any  point 

on  the  axis  of  a  circular  coil  varies  directly  with  the  current  and 
inversely  as  the  cube  of  the  slant  distance. 

If  the  point  P  be  moved  to  the  center  of  the  coil,  x  becomes 
equal  to  r  and  the  above  expression  becomes 

f  =  1.2* 
r 

Should  the  coil  consist  of  n  turns,  the  field  produced  is  n  times 
as  strong  as  that  produced  by. one  turn,  therefore,  the  above 
expressions  for  the  field  must  be  multiplied  by  n. 

An  important  consequence  follows  from  the  foregoing.  Since 
the  field  at  the  center  of  a  circular  coil  varies  directly  with  the 
current,  the  measure  of  the  field  may  be  used  as  a  measure  of  the 
current.  This  will  be  shown  in  the  following  paragraph. 

355.  Absolute  Unit  of  Current. — Since,  as  has  just  been  seen, 
we  obtain  the  intensity  of  the  field  at  the  center  of  the  coil  by 
adding  up  the  effects  produced  by  each  infinitesimal  section  of 
the  coil,  the  field  produced  by  a  portion  of  the  coil  must  be 


268  ELEMENTS  OF  ELECTRICITY. 

directly  proportional  to  the  length  of  this  portion,  or,  if  this 
length  be  I 

Ll 


If  in  this  expression  we  make  r  and  I  each  one  centimeter,  we 
have 

/=/ 

and  if  /  be  one  dyne,  /  is 

unity,  whence  we  derive  at  once  the  definition  of  the  absolute  unit 
of  current  as  that  current,  which  flowing  through  one  centimeter  of 
a  conductor  bent  into  the  arc  of  a  circle  whose  radius  is  one  centi- 
meter, exerts  a  force  of  one  dyne  upon  a  unit  pole  placed  at  the 
center  of  the  circle. 

If  in  Fig.  155  the  length  of  the 
conductor  from  a  to  6  be  one 
centimeter  and  if  it  be  bent  into 
the  arc  of  a  circle  of  one  centi- 
meter radius,  the  current  which 
flowing  through  this  conductor 
exerts  a  force  of  one  dyne  upon 
the  unit  pole  at  m,  has  a  strength 
of  one  absolute  unit. 

The  absolute  unit  of  current,  as  will  be  explained  later  (Chap. 
39),  is  ten  times  as  great  as  the  practical  unit,  the  ampere,  or, 
one  absolute  unit  equals  ten  amperes.  Therefore,  in  applying  the 
expressions  in  Pars.  353  and  354,  if  /  be  given  in  amperes,  it  must 
be  reduced  to  absolute  units  or  divided  by  ten  in  order  that  / 
should  be  in  dynes. 

356.  Force  Exerted  by  a  Magnetic  Field  upon  a  Conductor 
Carrying  a  Current. — The  force  exerted  upon  a  unit  pole  at  m  by 
the  field  of  ab  (Fig.  155)  is  shown  to  be 

LI 


If  the  strength  of  the  pole  be  m  instead  of  unity,  the  force  is 

._  m.I.l 

J  ~         ~2 


ELECTRO-MAGNETICS. 


269 


If  the  current  flows  as  shown  in  the  figure,  and  if  m  be  a  north 
pole,   this  force  acts  upward.     An  equal  downward  force  acts 

AM 

upon  ab.  In  the  above  expression  -y  is  the  field  along  ab  due  to 
the  pole  m  (Par.  136)  and  is  uniform.  Calling  this  H,  we  have 

f=I.H.l 

or,  the  force  exerted  by  a 

magnetic  field  upon  a 'con  due  tor  carrying  a  current  and  at  right 
angles  to  the  field  is  proportional  to  the  current,  to  the  intensity 
of  the  field  and  to  the  length  of  the  conductor.  This  force  is  at 
right  angles  to  the  field  and  to  the  conductor  and,  as  explained 
in  Par.  355,  is  expressed  in  dynes  when  I  is  in  absolute  units. 

Fig.  156  represents  a  cross-section  of  such  a  conductor  lying 
in  a  field  NS.    If  the  current  is  flowing  away  from  the  observer, 


Nl 


Fig.  156. 

the  lines  of  force  about  the  wire  are  clockwise,  therefore,  on  the 
upper  side  of  the  wire  they  coincide  in  direction  with  those  of  the 
field  but  on  the  lower  side  they  are  opposite  in  direction.  The 
field  is  therefore  distorted  as  shown,  the  lines  thickening  up  above 
the  wire  and  thinning  out  below.  Since  lines  of  force  have  a  ten- 
sion in  the  direction  of  their  length,  or  a  tendency  to  shorten,  the 
result  is  that  the  wire  is  urged  downward.  Application  of  the  left 
hand  rule  (Par.  352)  indicates  this  downward  motion. 

357.  Work  Done  in  Moving  Across  a  Magnetic  Field  a  Con- 
ductor Carrying  a  Current. — From  the  preceding  paragraph,  the 
force  exerted  upon  a  conductor  carrying  a  current  and  lying  at 
right  angles  to  the  field  is  I.  H.I  dynes. 


270  ELEMENTS  OF  ELECTRICITY. 

If  the  conductor  be  moved  at  right  angles  to  the  field  and  to  its 
own  length,  it  will  move  either  against  this  force  or  with  it.  In 
the  first  case,  work  must  be  done  upon  the  conductor;  in  the  second 
case,  work  is  done  by  the  conductor.  In  either  case,  if  the  dis- 
tance moved  be  x  centimeters  the  work,  being  force  X  path,  is 
W  =  I.H.l.xergs 

But  l.x  is  the  area  in  square  centimeters  swept  over  by  the  con- 
ductor in  its  movement,  H  is  the  number  of  lines  of  force  per  square 
centimeter  (Par.  145),  therefore  H.l.x  is  the  total  number  of  lines 
of  force  cut  by  the  moving  conductor.  Placing  this  equal  to  N  we 

have 

W  =  LNergs 

or  the  work  done  in  mov- 
ing across  a  magnetic  field  a  conductor  carrying  a  current  of  I 
absolute  units  is  equal  to  the  product  of  the  current  into  the  num- 
ber of  lines  of  force  cut. 

358.  Work  Done  in  Moving  Across  a  Magnetic  Field  a  Coil 
Carrying  a  Current. — This  is  merely  a  particular  case  of  the  fore- 
going but  furnishes  conceptions  which  facilitate  the  application 
of  the  principle  in  certain  deductions  which  we  shall  make  later  on. 
Suppose  the  moving  conductor  to  be  in  the  form  of  a  closed  coil 
and,  for  the  sake  of  simplicity,  suppose  this  to  be  rectangular  and 
to  be  moved  so  that  while  two  sides  cross  the  field  at  right  angles 
to  the  lines  of  force  the  other  two  sides  move  lengthwise  through 
the  field.  Since  these  latter  cut  no  lines  of  force  they  perform  no 
work.  If  the  field  be  uniform  each  of  the  other  two  sides  performs 
an  equal  amount  of  work,  but  the  current  in  them  flows  in  opposite 
directions  so  that  in  one  IN  is  positive  while  in  the  other  it  is 
negative.  The  net  result  is  zero,  or,  no  matter  how  it  may  be 
moved,  if  in  its  successive  positions  in  a  uniform  field  a  coil 
remains  parallel  to  its  original  position,  no  work  is  done. 

If,  however,  the  field  be  not  uniform,  the  work  done  by  one  of 
these  sides  will  be  IN  ergs,  that  by  the  other  —IN'  ergs,  and  the 
total  work  is  7  ( N  —  N')  ergs,  or  the  work  done  in  moving  a  coil 
in  a  magnetic  field  is  equal  to  the  product  of  the  current  in  the  coil 
into  the  change  in  the  number  of  lines  of  force  embraced  by  the 
coil.  This  is  general,  that  is,  it  is  true  whatever  the  shape  of  the 
coil  and  whether  its  motion  be  one  of  translation  or  of  rotation. 
It  also  follows  that  the  same  amount  of  energy  is  expended  if 


ELECTRO-MAGNETICS.  271 

the  coil  be  kept  ^motionless  and  the  field  embraced  be  moved  or 
varied. 

If  two  separate  and  similar  coils  be  moved  in  succession  across 
the  field,  the  work  done  by  each  is,  from  the  foregoing,  IN  ergs, 
in  which  N  is  the  change  in  the  number  of  lines  of  force  embraced 
by  the  coil,  the  total  work  being  21 N  ergs.  If  they  be  moved 
simultaneously  the  work  will  be  the  same.  Finally,  they  need 
not  be  separate  coils  but  may  be  two  turns  of  the  same  coil 
and  .still  the  work  will  be  21 N  ergs.  In  general,  therefore,  if  the 
field  within  a  coil  of  n  turns  carrying  a  current  I  be  increased 
or  decreased  by  N  lines  of  force,  the  work  done  will  be  nIN 
ergs. 

359.  Energy  Expended  upon  an  Electro- Magnetic  Field. — The 

conclusions  in  the  preceding  paragraph  are  irrespective  of  the 
origin  of  the  field.  It  may  therefore  be  produced  in  any  way,  even 
by  the  current  itself.  When  a  current  is  sent  around  a  coil,  N 
lines  of  force  are  produced  in  the  coil.  By  a  similar  method  to 
that  followed  in  Par.  96,  or  by  an  application  of  the  integral  cal- 
culus, it  may  be  shown  that  if  the  current  starts  at  zero  and  in- 
creases to  a  value  /,  the  energy  expended  in  establishing  the  field 
is  \  IN  ergs  over  and  above  that  spent  in  the  mere  heating  of  the 
conductor.  This  energy  is  absorbed  in  the  field  and  restored  when 
the  circuit  is  broken.  This  fact  explains  why  the  current  never 
rises  instantly  to  its  full  strength  when  the  circuit  is  closed  and 
also  why  the  current  always  lingers  after  the  circuit  is  broken, 
revealing  itself  as  a  spark.  This  subject  will  be  referred  to  again 
when  the  discussion  of  induction  is  reached. 

360.  Electro-Dynamics. — In  Par.  356  it  was  shown  that  a  con- 
ductor carrying  a  current  and  placed  in  a  magnetic  field  is  acted 
upon  by  a  force  at  right  angles  to  the  field  and  to  the  conductor. 
Since  conductors  carrying  currents  are  surrounded  by  magnetic 
fields  (Par.  346),  it  follows  that  if  two  such  conductors  be  placed 
near  together,  each  will  lie  in  the  magnetic  field  of  the  other  and 
each  will  be  subjected  to  a  force.    Ampere,  who  made  this  dis- 
covery in  1820,  applied  the  term  electro-dynamics  to  that  branch 
of  electricity  which  treats  of  the  forces  exerted  between  currents, 
and  formulated  the  laws  given  in  the  following  paragraphs. 

361.  Force  Exerted  Between  Conductors  Carrying  Currents. — 

Two  parallel  conductors  attract  one  another  if  the  currents  in  them 


272 


ELEMENTS  OF  ELECTRICITY. 


flow  in  the  same  direction  but  repel  each  other  if  the  currents  flow 
in  opposite  directions. 

A  and  B,  Fig.  157,  are  two  such  conductors.  Considering  B  as 
lying  in  the  field  about  A,  application  of  the  left  hand  rule  (Par. 
352)  will  show  that  B  is  urged  at  right  angles  to  its  length  and 


Fig.  157. 

towards  A.  Similarly,  A  is  urged  towards  B.  Had  the  currents 
flowed  in  opposite  directions  the  wires  would  have  repelled  each 
other. 

It  may  be  shown  by  Laplace's  law  (Par.  353)  that  if  the  two 
wires  be  not  parallel,  the  electro-magnetic  effect  of  either  current 
can  be  resolved  into  two  components,  one  parallel  to  the  remain- 
ing current,  the  other  perpendicular  to  it  and  contributing  noth- 
ing to  the  forces  between  the  two  wires.  In  the  most  general 
case,  therefore,  if  two  .conductors  cross,  those  portions  in  which 
both  currents  flow  either  towards  or  from  the  point  of  crossing 
attract  each  other  while  those  portions  in  which  one  current  flows 
towards  and  the  other  from  the  point  of  crossing  repel  each 
other. 

It  is  not  necessary  that  the  two  conductors  be  parts  of  different 
circuits.  The  same  law  applies  to  portions  of  a  single  circuit.  If, 
for  example,  a  current  be  passed  through  a  helical  coil,  the  adjacent 
turns  attract  each  other  and  the  coil  tends  to  shorten. 


ELECTRO-MAGNETICS.  273 

362.  Intensity  of  Force  Between  Parallel  Conductors  Carrying 
Currents.  —  If  the  wire  A,  Fig.  157,  be  of  indefinite  length  and  if 
there  be  flowing  in  it  a  current  of  strength  /',  the  intensity  of  the 
field  produced  by  it  at  any  point  along  B  is  (Par.  353) 


r  being  the  distance  between 

the  two  wires.  But  we  have  seen  (Par.  356)  that  the  force  exerted 
by  a  field  H  upon  a  wire  of  length  I  carrying  a  current  of  strength 
/  is  /  =  /.  H  .1.  Substituting  in  this  the  value  of  H  from  above,  we 
have 

f  _  2in 

J=      r 

or  the  force  exerted  upon 

the  second  wire  B  is  directly  proportional  to  the  product  of  the 
currents  in  the  two  wires  and  to  the  length  of  B  and  inversely 
proportional  to  the  simple  distance  between  the  wires. 


274  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  30. 
GALVANOSCOPES   AND   GALVANOMETERS. 

363.  Galvanoscopes. — Oerstedt's  discovery  affords  us  a  means 
of  determining  whether  or  not  a  current  is  flowing  in  a  conductor, 
and  if  flowing,  in  what  direction.    For  example,  in  the  case  of  an 
electric  wire  crossing  the  ceiling  of  a  room,  it  is  only  necessary  to 
hold  a  magnetic  needle  an  inch  or  so  below  the  wire  when,  if  a  cur- 
rent is  flowing,  the  needle  will  be  deflected  and  the  direction  of 
this  deflection,  in  conjunction  with  the  right  hand  rule,  will  reveal 
the  direction  of  flow  of  the  current.    Instruments  designed  to  give 
information  of  this  character  are  called  galvanoscopes. 

364.  Increase  of  Sensitiveness.  —  We  frequently  have  to  deal 
with  currents  so  small  that  the  deflection  they  produce  in  an 
ordinary  needle  is  imperceptible.    In  such  cases  the  only  remedy 
is  to  increase  the  sensitiveness  of  the  instrument.    A  needle  when 
in  use  is  acted  upon  by  two  forces;  first,  the  deflecting  force  which 
causes  it  to  move  and,  second,  the  controlling  force  which  resists 
deflection.    We  therefore  have  two  expedients;  we  may  multiply 
the  effect  of  the  deflecting  force  or  we  may  weaken  the  controlling 
force.     The  highest  degree  of  sensitiveness  is  attained  by  com- 
bining these  two.    We  shall  now  examine  these  in  detail. 

365.  Schweigger's  Multiplier. — Suppose  a  needle  to  be  placed  at 
the  center  and  to  lie  in  the  plane  of  a  vertical  coil.    Application  of 
the  right  hand  rule  will  reveal  the  fact  (shown  already  in  Par. 
354),  that  when  the  circuit  is  closed,  the  top,  the  sides,  the  bottom 
of  the  coil,  all  contribute  to  produce  a  deflection  of  the  needle  in 
one  and  the  same  direction.    As  the  palm  of  the  right  hand  is  slid 
along  the  coil,  the  thumb  points  constantly  in  the  same  direc- 
tion which  is  that  of  every  line  of  force  enclosed  by  the  coil.    If, 
therefore,  instead  of  simply  passing  the  wire  by  the  needle,  as  in 
Oerstedt's  experiment,  we  take  a  turn  entirely  around  it,  the  de- 
flecting force  is  very  much  increased.     Finally,  we  need  not  stop  at 
one  loop.    Every  succeeding  turn  adds  its  lines  of  force  to  those 
already  in  the  field  and  we  may,  therefore,  use  a  coil  of  a  great 


ELECTRO-MAGNETICS. 


275 


many  turns  and  multiply  by  just  so  much  the  effects  of  the  cur- 
rent. Such  is  the  principle  of  Schweigger's  multiplier  (Fig.  158) 
which  consists  of  a  suitable  frame  which  may  be  rectangular,  oval 
or  circular  and  around  which  are  wrapped  many  turns  of  insulated 


Fig.  158. 

wire.  The  frame  must  be  of  some  non-magnetic  material  such  as 
wood,  ebonite,  brass,  etc.,  otherwise  it  would  acquire  magnetism 
from  the  current.  In  the  center  of  the  coil  is  pivoted  the  needle 
whose  deflection  is  to  be  observed. 

A  multiplier  should  be  used  with  feeble  currents  only.  With  a 
strong  current  it  is  not  necessary;  moreover,  the  resistance  of  the 
many  turns  of  wire  would  cut  down  a  large  current.  It  is  true 
that  it  also  reduces  a  small  current  but  not  so  much  proportionally. 
The  general  rule  is  that  a  multiplier  is  used  when  the  circuit 
already  contains  great  resistance  but  should  not  be  used  if  the 
resistance  be  small. 

366.  Methods  of  Weakening  Controlling  Force. — The  second 
method  of  rendering  a  needle  more  sensitive,  the  weakening  of  the 
controlling  force,  may  be  applied  in  two  ways: 

(a)  Haiiy's  method.     The  earth's  controlling  force  may  be 
very  nearly  neutralized,  there  being  left  a  small  excess  just  suffi- 
cient to  control  the  needle. 

(b)  Astatic  combinations.    The  earth's  controlling  force  may 
be  entirely  neutralized,  and  some  very  feeble  force,  such  as  the 
torsion  of  a  silk  fibre,  substituted  therefor. 

367.  Haiiy's  Method. — Hauy's  method  of  weakening  the  earth's 
control  is  shown  diagrammatically  in  Fig.  159  as  being  applied  to 
the  needle  of  Schweigger's  multiplier.    The  needle  is  suspended  in 


276 


ELEMENTS  OF  ELECTRICITY. 


the  center  of  the  multiplier,  the  plane  of  the  coil  being  in  the 
magnetic  meridian.  A  brass  rod  AB  projects  upward  from  the 
top  of  the  coil  and  upon  this  rod  there  slides  a  bar  magnet  NS, 
usually  curved  as  shown.  Now,  as  this  bar  magnet  ir  slid  down 
towards  the  coil,  its  north  pole  repels  with  an  increasing  force  the 


Fig.  159. 

north  pole  of  the  needle.  A  point  is  finally  reached  where  NS 
exactly  counterbalances  the  earth's  controlling  force  upon  the 
needle  and  if  this  point  be  passed  the  needle  is  reversed.  By  stop- 
ping the  bar  magnet  just  above  this  critical  point,  the  effect  of  the 
earth's  control  may  be  reduced  to  a  minimum.  This  method  is 
employed  in  Thompson's  mirror  galvanometer  (Par.  377). 

368.  Astatic  Combinations. — Two  needles  of  equal  size  and 
strength  fastened  rigidly  together  in  reversed  positions  and  with 
their  axes  parallel  constitute  an  astatic  pair  (Fig.  160).  This  com- 
bination is  independent  of  the  earth's  control  and  the  controlling 
force  is  generally  the  torsion  of  a  fine  silk  fibre  by  which  the  needles 
are  suspended.  They  are  usually  mounted  so  that  the  lower  needle 
swings  in  the  center  of  a  multiplier,  the  upper  needle  travelling 
over  a  graduated  scale  on  the  top  of  the  coil  and  thus  serving  as  a 
pointer.  Application  of  the  right  hand  rule  will  show  that  the 


ELECTRO-MAGNETICS. 


277 


current  in  the  portion  of  the  coil  between  the  two  needles  will 
cause  them  both  to  rotate  in  the  same  direction.  By  using  a  coil 
wrapped  like  a  figure  eight,  both  needles  may  be  surrounded  by 
coils. 


N 


Fig.  160. 

There  are  a  number  of  other  astatic  combinations.  A  suspended 
horseshoe  magnet  is  astatic  and  may  be  used  as  an  astatic  pair. 

369.  Magnetic  Shells. — Should  we  be  able  to  cut  from  the  end 
of  a  bar  magnet  a  thin  slice,  and  should  this  slice  preserve  its 
original  polarity,  we  would  have  a  magnetic  shell,  a  thin  piece  of 
metal,  one  face  of  which  would  be  of  north  polarity,  the  other 
south. 

Another  conception  of  a  magnetic  shell  is  to  suppose  that  we 
had  a  great  number  of  very  small  magnets,  like  minute  type,  and 
that  we  should  arrange  them  over  the  area  of  a  circle  side  by  side 


Fig.  161. 

like  the  cells  of  a  honeycomb  (Fig.  161),  the  north  poles  all  point- 
ing up,  the  result  would  be  a  magnetic  shell.  If  a  coil  of  wire  be 
bent  into  a  circle  of  the  same  size  as  the  shell,  a  current  could  be 
sent  through  the  wire  which  would  produce  inside  the  coil  as  many 
lines  of  force  as  emerged  from  the  shell.  Since  we  have  shown  (Par. 
365)  that  these  lines  all  emerge  from  one  face  of  the  coil  and  in  the 
same  direction,  the  coil  and  the  shell  are  magnetically  equivalent 
to  each  other.  Coils  carrying  a  current  behave  in  many  ways  as 


278 


ELEMENTS  OF  ELECTRICITY. 


if  they  were  magnets.  They  have  polarity  and  will  attract  or 
repel  a  magnet,  depending  upon  the  pole  of  the  magnet  and  the 
face  of  the  coil  to  which  it  is  presented.  They  also  attract  or  repel 
each  other. 

This  conception  of  a  magnetic  shell  is  used  in  mathematical  dis- 
cussions of  electricity.  We  will  not  have  occasion  to  use  it  further 
but  there  follows  from  it  a  very  important  principle  which  we  shall 
now  develop. 

370.  De  La  Rive's  Floating  Battery.— One  form  of  De  La  Rive's 
floating  battery  is  represented  in  Fig.  162.  It  consists  of  a  turnip- 
shaped  glass  cell  with  a  constricted  lower  part  containing  dilute 
acid.  Upon  a  cork  in  the  mouth  of  the  cell  is  mounted  a  vertical 


Fig.  162. 

coil  of  wire  of  a  number  of  turns,  the  ends  of  this  coil  extending 
below  the  cork  and  terminating,  one  in  a  copper,  the  other  in  a 
zinc  plate  which  dip  into  the  acid.  The  arrangement  is  therefore 
seen  to  be  only  a  simple  cell,  the  coil  constituting  the  external  cir- 
cuit. The  cell  is  placed  in  a  basin  of  water  so  that  it  floats  freely. 
If  the  current  flows  around  the  coil  in  the  direction  indicated  by 
the  arrow,  the  lines  of  force  of  the  coil  pass  through  from  right  to 
left,  or,  from  what  we  have  just  seen,  the  coil  is  equivalent  to  a 
magnetic  shell  whose  north  face  is  to  the  left. 

Suppose  that,  as  represented  in  the  figure,  the  north  pole  of  a 
bar  magnet  be  presented  to  the  north  face  of  the  coil.    The  float- 


ELECTRO-MAGNETICS. 


279 


ing  cell,  as  was  to  be  expected,  will  back  away  or  recede,  but,  more 
than  this,  it  will  turn  around  until  its  south  face  is  presented  and 
will  then  approach  the  magnet  and,  instead  of  stopping  when  it 
has  reached  the  pole,  will  continue  to  advance  and  will  thread 
itself  upon  the  magnet  until  it  has  reached  the  middle  point.  Its 
lines  of  force  and  those  of  the  magnet  now  coincide  in  direction. 
It  is  now  in  a  position  of  stable  equilibrium  for  if  it  be  pushed 
towards  either  end  of  the  magnet  and  released  it  will  immediately 
return  to  its  median  position.  On  the  other  hand,  suppose  the 
coil  to  be  held  and  the  magnet  thrust  into  it  in  reversed  direction, 
that  is,  with  its  lines  of  force  opposite  in  direction  to  those  of  the 
coil.  If  the  coil  be  released  when  exactly  at  the  center  of  the 
magnet  it  will  remain,  but  it  is  in  unstable  equilibrium,  for  if  dis- 
placed ever  so  slightly  in  either  direction  from  this  central  position 
it  will  slip  off  the  magnet,  turn  around  and  return. 

One  of  these  cells  floating  freely  in  a  vessel  of  water  will  finally 
come  to  rest  with  the  axis  of  the  coil  in  a  north  and  south  position, 
that  is,  with  its  field  coinciding  in  direction  with  that  of  the  earth. 
Two  such  cells  will  move  about  until  the  fields  of  their  coils  coin- 
cide in  direction. 

371.  Maxwell's  Law. — The  principle  in  accordance  with  which 
the  movements  described  in  the  preceding  paragraph  take  place 


Fig.  163. 

has  been  formulated  by  Maxwell  to  the  effect  that  every  electro- 
magnetic system  tends  to  change  its  configuration  so  that  the  exciting 
circuit  will  embrace  in  a  positive  direction  the  maximum  number  of 
lines  of  force.  This  law  applies  to  all  combinations  of  closed  cir- 
cuits and  magnetic  fields,  whether  these  fields  be  produced  by 
magnets,  by  other  circuits,  or  even  by  the  circuit  itself.  This  last 
is  shown  by  an  experiment  devised  by  Ampere.  In  a  wooden  block 
(Fig.  163)  there  are  hollowed  out  two  parallel  troughs  which  are 


280  ELEMENTS  OF  ELECTRICITY. 

then  filled  with  mercury.  A  wire  bent  as  shown  is  then  placed  as 
a  bridge  with  one  end  in  each  trough  and  floats  on  the  surface  of 
the  mercury.  The  current  entering  at  A  crosses  this  bridge  and 
leaves  by  B,  the  lines  of  force  in  this  rectangular  area  all  pointing 
up  as  shown  by  the  arrows.  As  soon  as  the  circuit  is  closed,  the 
wire  floats  off  towards  C,  thereby  increasing  the  area  ACB  and 
consequently  the  number  of  lines  of  force  embraced  by  the  circuit. 
The  majority  of  the  instruments,  shortly  to  be  described, 
operate  in  accordance  with  this  law  and  it  also  explains  the  move- 
ment of  all  motors.  It  has  already  been  shown  (Par.  144)  that, 
in  a  more  general  form,  it  accounts  for  the  position  assumed  by 
magnetic  needle. 

372.  Galvanometers. — A  galvanoscope  indicates  by  the  move- 
ment of  its  needle  both  that  a  current  is  flowing  and  the  direction 
of  its  flow.  If  this  movement  also  affords  a  measure  of  the  strength 

of  the  current,  the  instrument  is 
called  a  galvanometer.  There  are 
many  varieties  of  galvanometers 
but  they  may  all  be  classed  under 
one  of  two  heads:  first,  those  in 
which  a  needle  moves  in  a  field 
produced  by  a  fixed  coil  and, 
second,  those  in  which  there  is 
no  needle  but  a  suspended  coil 
which  swings  in  a  fixed  field. 
Of  the  latter  class,  the  field  may 
be  produced  by  a  permanent 
magnet  or  by  a  fixed  coil.  We 
shall  now  describe  examples  of 
each  of  the  above. 

373.  The  Tangent  Galvanom- 
eter.—This  is  an  example  of  a 
galvanometer  of  the  first  class, 
that  is,  one  with  a  needle  mov- 
ing in  a  field  produced  by  a  fixed 
Fig  164  coil.  It  consists  (Fig.  164)  of  a 

vertical  circular  coil,  more  than 
one  foot  in  diameter,  mounted  upon  a  base  by  which  it  may  be 
accurately  placed  in  the  magnetic  meridian.  The  coil  is  composed 


ELECTRO-MAGNETICS.  281 

of  a  single  turn  of  heavy  copper  wire  or  copper  ribbon.  For 
measuring  small  currents  it  may  consist  of  many  turns  of  fine 
wire.  Pivoted  at  the  center  of  this  coil  is  a  short  thick  needle, 
generally  less  than  an  inch  in  length.  Since  it  would  be  very 
difficult  to  read  with  any  accuracy  a  scale  engraved  upon  a  circle 
whose  diameter  is  only  one  inch,  the  needle  is  usually  prolonged 
by  light  aluminum  pointers.  These  have  no  magnetic  effect  but 
permit  the  use  of  a  much  larger  graduated  scale. 

374.  Measurement  of  Current  by  Tangent  Galvanometer. — In 

order  to  measure  a  current  by  the  tangent  galvanometer,  the  latter 
is  connected  up  in  the  circuit,  its  coil  accurately  placed  in  the  mag- 
netic meridian,  the  circuit  closed  and  the  angle  of  deflection  of  the 
needle  read.  If  it  be  convenient  to  reverse  the  current,  this  is  done, 
the  new  angle  of  deflection  read  and  the  mean  of  the  two  readings 
is  taken  as  the  correct  one. 

In  Par.  146  we  saw  that  "the  magnetic  field  which,  acting  at 
right  angles  to  the  meridian,  produces  in  a  needle  a  deflection  5,  is 
equal  to  the  horizontal  component  of  the  earth's  magnetism  at  that 
point  multiplied  by  the  tangent  of  the  angle  of  deflection,"  or 


Again,  in  Par.  354  we  saw  that  the  field  produced  at  the 
center  of  a  circular  coil  of  radius  r  by  a  current  of  /  absolute 
units  is 

r     f.ftf 

J  ~      r 

We  therefore  have 

1 .2-JT 


whence 

/  =  £-  .H. tan  6 

In  this  r  is  determined  by  measurement  of  the  coil,  H  is 
obtained  from  observation  (Par.  148),  or  from  a  table  (Par.  175), 
6  is  read  from  the  galvanometer  scale  and  tan  6  is  obtained  from  a 
table. 

If  the  galvanometer  coil  has  n  turns,  the  second  expression  for  / 


-        .  r™      f 

becomes    /  = .     The  factor  — ,  since  it  depends  purely 


282 


ELEMENTS  OF  ELECTRICITY. 


upon  the  dimensions  of  the  instrument,  is  called  the  galvanometer 
constant.  Calling  this  G,  we  have 

/=/.G 

whence,  if  7  =  1,  f=G,  or  the 

galvanometer  constant  is  equal  to  the  strength  of  the  field  pro- 
duced at  the  center  of  the  coil  by  a  current  of  one  absolute  unit. 

In  practice,  it  is  more  frequent  to  use  the  tangent  galvanometer 
to  compare  currents  rather  than  to  determine  them  absolutely. 
Various  currents  are  to  each  other  as  the  tangents  of  the  angles  of 
deflection  which  they  severally  produce.  If  the  deflection  pro- 
duced by  a  known  current  be  ascertained,  the  determination  of 
other  currents  is  a  simple  matter. 

375.  Remarks  on  Principle  of  Tangent  Galvanometer. — The 
deduction  in  the  preceding  paragraph  is  based  upon  two  assump- 
tions, neither  of  which  is  strictly  accurate,  although  the  error  is 


/  /  v^--^,}X 

1     '    I  \  vA^/ir/"}   ;  i 
*      \    **S~£?jf/ti    i   ' 

^O;;:<'''/  /  , 
**•.» ^  /  /  /   / 


Fig.  165. 


usually  negligible.  First,  the  deflecting  force  is  supposed  to  be 
perpendicular  to  the  meridian.  Fig.  165  represents  the  field  along 
the  horizontal  diameter  of  the  coil  of  a  tangent  galvanometer, 
whence  it  is  seen  that  the  lines  of  force  are  curves  (although 
slightly  different  from  the  circles  shown  in  the  figure),  and  there- 
fore are  perpendicular  to  this  meridian  only  where  they  pierce 
the  plane  of  the  coil.  They  have,  however,  less  curvature  near  the 
center  of  the  field  and  this  flatness  increases  with  the  diameter  of 
the  coil,  for  which  reason  the  needle  is  made  very  short  and  the 
coil  large.  A  still  better  remedy  is  to  use  two  parallel  coils  and 
place  the  needle  midway  between  them.  The  lines  of  force  of  the 
field  in  this  case  are  sensibly  parallel. 

Second,  the  expression  employed  for  the  intensity  of  the  field  is 
determined  for  the  center  of  the  coil  (Par.  354).    The  field,  as  in- 


ELECTRO-MAGNETICS. 


283 


dicated  in  the  figure,  is  much  stronger  near  the  coil  and  diminishes 
towards  the  center.  The  needle  is  therefore  made  short  so  that 
its  poles  do  not  extend  into  a  field  much  stronger  than  that  at  the 
actual  center. 

376.  The  Sine  Galvanometer. — The  sine  galvanometer,  shown 
in  its  simplest  form  in  Fig.  166,  differs  from  the  tangent  gal- 
vanometer only  in  that  the  coil  need  not  be  so  large  and  that 
the  needle  extends  as  nearly  across  the  diameter  of  the  coil  as  its 


Fig.  166. 


surrounding  graduated  circle  will  permit.  The  poles  of  the  needle 
therefore  lie  in  the  strong  field  close  to  the  coil  and  the  instrument 
is  more  sensitive  than  the  tangent  galvanometer.  The  coil  is  free 
to  rotate  about  a  vertical  axis  and  in  more  improved  forms  of  the 
instrument  there  is  a  horizontal  graduated  limb  from  which  may 
be  read  by  a  vernier  the  exact  angle  through  which  the  coil  has 
been  turned.  This  limb,  however,  is  not  essential. 

To  use  the  instrument  to  measure  a  current,  it  is  connected  up 
in  the  circuit  and  accurately  adjusted  until  the  coil  lies  in  the  mag- 
netic meridian.  The  horizontal  graduated  limb  is  then  read  and 
the  circuit  is  closed,  causing  a  deflection  of  the  needle.  The  coil 
is  then  turned  by  hand  in  the  direction  of  the  deflection  of  the 


284  ELEMENTS  OF  ELECTRICITY. 

needle  until  the  needle  is  overtaken  and  lies  once  more  in  the  plane 
of  the  coil.  The  deflecting  force,  or  the  field  of  the  coil,  is  now  per- 
pendicular to  the  needle.  The  angle  through  which  the  coil  has 
been  turned  is  read  from  the  scale  on  the  horizontal  limb.  Should 
there  be  no  horizontal  limb,  this  angle  can  still  be  determined,  for 
it  is  only  necessary  to  take  the  reading  of  the  needle,  then  break 
the  circuit  and  take  the  reading  of  the  needle  when  it  has  swung 
back  into  the  meridian;  the  difference  between  these  two  readings 
is  the  required  angle. 

In  Par.  147  it  was  shown  that  "magnetic  fields  acting  at  a 
cvastant  angle  with  the  needle  are  to  each  other  as  the  sines  of  the 
respective  angles  of  deflection."  It  follows  that  the  current  is 
proportional  to  the  sine  of  the  angle  through  which  the  coil  has 
been  turned;  also,  that  different  currents  are  to  each  other  as  the 
sines  of  these  angles.  The  sine  galvanometer  can  therefore  be 
used  to  compare  currents  although  it  can  not  be  used,  like  the 
tangent  galvanometer,  to  measure  currents  absolutely. 

Should  the  deflecting  force  be  greater  than  the  controlling  force, 
the  coil  will  never  overtake  the  needle,  and  in  such  a  case  the 
instrument  can  not  be  used. 

377.  The  Mirror  Galvanometer. — The  mirror  galvanometer  is 
an  extremely  sensitive  form  of  instrument  and  is  more  frequently 
used  as  a  galvanoscope  than  as  a  galvanometer,  in  fact,  it  was 
devised  by  Lord  Kelvin  to  give  indications  of  the  exceedingly  small 
currents  transmitted  by  submarine  cables.  Its  principle  will  be 
understood  from  Fig.  159.  It  consists  of  a  vertical  coil  of  many 
thousand  turns  of  very  fine  insulated  wire.  The  opening  through 
the  coil  is  barely  half  an  inch  in  diameter  and  in  the  center  of  this 
there  hangs,  by  a  silk  fibre,  a  very  light  glass  mirror,  about  the 
size  of  a  silver  ten-cent  piece.  The  mirror  is  slightly  concave  so  as 
to  focus  in  a  long  pencil  any  rays  of  light  which  fall  upon  it.  To 
the  back  of  this  mirror  there  are  glued  three  or  four  very  light 
magnets  made  of  short  sections  of  watch  spring.  The  controlling 
force  of  the  earth's  magnetism  is  neutralized  by  Haiiy's  method. 
The  little  mirror  normally  hangs  with  its  plane  parallel  to  the 
face  of  the  coil,  but  when  a  current  passes  through  the  coil  the 
magnets  at  the  back  of  the  mirror  tend  to  turn  in  accordance  with 
Maxwell's  law  until  their  lines  of  force  coincide  with  those  of  the 
coil.  A  beam  of  light  is  caused  to  fall  upon  the  mirror  and  is 
reflected  back,  producing  a  bright  spot  upon  a  blank  wall  or  upon 


ELECTRO-MAGNETICS. 


285 


a  suitably-prepared  scale.  The  slightest  angular  motion  of  the 
mirror  is  revealed  at  once  by  motion  of  the  spot  of  light,  the 
angular  motion  of  the  spot  being  twice  that  of  the  mirror  and 
the  radius  being  the  distance  from  the  mirror  to  the  wall  or  scale. 
Thompson  states  that  the  most  improved  form  of  this  instrument 
gives  indications  of  a  current  as  small  as  one  fifty-four-thousand 
millionth  of  an  ampere. 

378.  Suspended  Coil  Galvanometer. — In  the  galvanometers 
described  in  the  preceding  paragraphs,  the  coil  carrying  the  cur- 
rent is  fixed  and  the  magnet  rotates;  in  the  form  now  to  be  de- 
scribed the  magnet  is  fixed  and  the  coil  rotates.  While  not  having 
the  extreme  delicacy  of  the  mir- 
ror galvanometer,  the  suspended 
coil  galvanometer  is  still  of  a  high 
order  of  sensitiveness  and  is  used 
by  practical  electricians  where  the 
most  refined  observations  are  re- 
quired. There  are  many  different 
forms  and  it  is  known  by  other 
names,  such  as  the  D' Arson val 
galvanometer,  the  reflecting  gal- 
vanometer, etc.,  but  the  principle 
of  all  is  the  same. 

A  usual  form  consists  (Fig.  167) 
of  a  heavy  rectangular  frame 
of  magnetized  steel  whose  poles 
are  N  and  S.  This  frame  is 
mounted  upon  a  wooden  back  C 
which  may  be  fastened  to  a  wall, 
mounted  upon  a  tripod,  or  other- 
wise suitably  supported.  Through 
the  center  of  the  top  of  the  frame 
is  bored  a  hole  into  which  is 
screwed  a  vertical  brass  tube  D. 
In  the  upper  end  of  this  tube 
there  fits  a  small  brass  spindle 
with  a  cross-bar  handle  E.  This  spindle  may  be  turned  about  a 
vertical  axis  and  may  be  raised  or  lowered  and  fastened  in  any 
desired  position  by  the  set-screw  shown  at  the  right.  The  mov- 
able coil  is  suspended  from  the  spindle  by  means  of  a  very  delicate 


Fig.  167. 


286  ELEMENTS  OF  ELECTRICITY. 

phosphor-bronze  filament.  Silk  or  quartz  fibres  can  not  be  used 
since  the  suspension  must  convey  current  to  the  coil.  The 
coil,  which  swings  in  the  space  between  the  poles,  consists  of 
many  turns  of  very  fine  wire  wrapped  upon  a  thin,  light, 
elongated  rectangular  metal  frame.  Midway  between  the  poles 
N  and  S  there  is  fastened  to  the  wooden  back  C  a  vertical 
soft-iron  cylinder  K  which  projects  into  the  opening  of  the  coil 
frame,  almost  entirely  filling  this  space  and  leaving  barely  room 
for  the  coil  to  turn.  This,  as  shown  in  Fig.  69,  Par.  143,  greatly 
concentrates  the  field  in  which  the  coil  moves.  Above  the  coil 
frame  and  supported  by  it  is  a  small  mirror  F.  Below  the  coil,  a 
coiled  phosphor-bronze  filament  connects  to  a  small  metal  bracket 
G  which  in  turn  is  connected  from  behind  to  the  binding  post  B. 
The  other  binding  post  A  is  connected  direct  to  the  steel  frame. 
A  current  entering  at  A  travels  up  the  steel  frame  to  the  brass 
tube,  thence  up  this  tube  to  the  spindle,  thence  down  the  suspen- 
sion to  the  coil,  around  the  coil,  thence  through  the  lower  filament 
to  G  and  out  by  B.  The  coil  hangs  normally  with  its  face  to  the 
front,  the  controlling  force  being  the  torsion  of  the  phosphor- 
bronze  suspension.  If  the  coil  does  not  hang  properly,  it  can  be 
made  to  do  so  by  turning  the  spindle  E.  With  the  poles  situated 
as  represented  in  the  figure,  the  lines  of  force  of  the  field  run  from 
right  to  left.  When  a  current  flows  through  the  coil,  the  lines  of 
force  of  the  coil  are  from  front  to  rear,  or  the  reverse;  therefore, 
the  coil,  in  accordance  with  Maxwell's  law,  turns  either  to  the 
right  or  left.  The  coil,  mirror  and  filaments  are  protected  by  a 
metal  plate  screwed  to  the  frame  and  carrying  a  glass  window 
through  which  the  mirror  may  be  observed. 

In  using  the  instrument,  there  is  attached  to  the  hooks  H  H  an 
arm  (Fig.  168)  which  carries  at  its  farther  end  a  telescope  and  a 
printed  scale.  The  scale,  which  is  usually  divided  into  millimeters, 
is  one-half  meter  from  the  mirror.  By  means  of  the  telescope  the 
reflection  of  the  scale  in  the  mirror  is  observed.  Since  the  tele- 
scope inverts  objects  and  the  mirror  reverses  them  right  for  left, 
the  numbers  on  the  scale  must  be  engraved  both  upside  down  and 
reversed.  Cross  hairs  in  the  telescope  allow  the  scale  to  be  read 
very  accurately.  When  the  coil,  and  consequently  the  mirror,  is 
deflected  by  a  current,  it  appears  to  the  eye  of  the  observer  as  if 
the  scale  moved  across  the  field  of  the  telescope.  For  moderate 
deflections  of  the  coil  the  currents  producing  these  deflections  are 


ELECTRO-MAGNETICS. 


287 


proportional  to  the  number  of  scale  divisions  passed  over  by  the 
vertical  hair. 


Fig.  168. 


379.  Damping. — In  instruments  in  which  readings  are  taken  of 
the  angular  displacement  of  a  needle,  a  coil,  or  a  mirror,  the  mov- 
ing part  may  oscillate  for  some  time  before  coming  to  its  final 
position  of  rest.  This  causes,  in  taking  observations,  a  vexatious 
delay  which  it  is  very  desirable  to  avoid.  Any  process  by  which, 
while  not  interfering  with  the  freedom  of  movement  of  the  part, 
it  is  made  to  come  to  rest  quickly  is  called  "damping"  and  an 
instrument  whose  needle  moves  at  once  to  the  proper  reading  on 
the  scale  is  said  to  be  "dead  beat"  Damping  may  be  brought  about 
by  (a)  mechanical  means  or  (b)  electrical  means.  As  an  example 
of  mechanical  damping,  a  moving  coil  may  have  suspended  below 
it  a  metal  vane  which  is  immersed  in  oil,  the  viscosity  of  the  liquid 
slowing  down  the  movement  and  preventing  vacillation.  Sus- 
pended coil  galvanometers  often  have  attached  to  the  mirror  a 
thin  sheet  of  metal  or  mica  which  turns  in  a  little  closed  box  which 
it  nearly  fits.  The  confined  air  in  this  box  acts  something  like  the 
oil  in  the  first  case. 

Electrical  damping  can  not  be  thoroughly  explained  at  present 
but  depends  upon  the  principle  that  a  piece  of  metal  moved  in  a 
magnetic  field  experiences  forces  which  tend  to  stop  the  movement 
(Par.  430).  This  is  the  method  employed  in  the  suspended  coil 
galvanometer  just  described.  The  metal  frame  upon  which  the 
coil  is  wrapped  turns  in  the  strong  magnetic  field  between  the  poles 
and  the  soft-iron  core  and  is  thus  brought  quickly  to  rest. 


288  ELEMENTS  OF  ELECTRICITY. 

380.  Need  of  Galvanometer  Shunts. — The  currents  which  a 
reflecting  galvanometer  may  measure  are  extremely  small.    Thus, 
if  a  pin  be  connected  by  a  wire  to  one  terminal  of  the  galvanometer 
and  a  needle  be  connected  to  the  other  and  the  pin  and  needle  be 
held  tightly  between  the  fingers,  the  contact  of  the  two  dissimilar 
metals  with  the  slight  moisture  of  the  fingers  will  drive  a  sufficient 
current  through  the  coil  to  cause  the  mirror  to  run  entirely  off  the 
scale.    In  order  therefore  to  measure  even  minute  currents  we  must 
employ  a  shunt  by  which,  as  explained  in  Par.  301,  only  one-tenth, 
one-hundredth,  or  one-thousandth  of  the  total  current  is  permitted 
to  flow  through  the  instrument.    Even  in  this  case  it  is  usual  to 
insert  in  the  circuit  a  resistance  of  50,000  or  100,000  ohms  by 
which  the  current  is  reduced  to  measurable  intensity. 

381.  The  Universal  Shunt.— We  saw  in  Par.  301  that  the  resist- 
ance of  a  galvanometer  shunt  must  bear  a  fixed  relation  to  the  re- 
sistance of  the  galvanometer  with  which  it  is  used  and  that  shunts 
are  not  interchangeable  and  can  be  used  only  with  the  galvanom- 
eter for  which  they  are  constructed.     The  phosphor-bronze  sus- 
pension of  a  suspended  coil  galvanometer  is  frequently  broken  and 
must  be  replaced  by  a  new  one,  in  doing  which  the  resistance  of 
the  galvanometer  is  usually  considerably  changed  and  this  change 
would  render  useless  a  shunt  designed  to  accompany  the  original 
resistance.    Reflection  will  show,  however,  that  if  we  simply  wish 
to  compare  currents  relatively  it  is  not  necessary  to  know  what 
fraction  of  the  total  current  flows  through  the  galvanometer,  for 
if  1/xth  of  a  current  /'  flowing  through  a  galvanometer  produces 
a  certain  deflection,  and  if  1/xth  of  a  different  current  I"  produces 
a  deflection  twice  as  great,  then  the  current  /"  is  twice  as  great 
as  the  current  /'. 

Carrying  out  the  idea  farther,  Ayrton  devised  a  universal  shunt 
which  may  be  used  with  any  galvanometer  and  which  can  be  so 
varied  that,  irrespective  of  the  resistance  of  the  galvanometer,  the 
deflection  produced  is  proportional  to  one- tenth,  one-hundredth, 
or  one- thousandth,  etc.,  of  the  total  current.  This  shunt  is  shown 
diagrammatically  in  Fig.  169.  Five  contacts  (sometimes  six)  are 
arranged  in  the  arc  of  a  circle  and  marked,  1,  TV,  TK>  T<jV<j  and  0. 
Between  these  contacts  are  resistance  coils  A,  B,  C,  D.  If  R  be 
the  total  resistance,  A  is  .9  of  R,  A +B  is  .99  of  R  and  A+B-fC 
is  .999  of  R.  A  common  arrangement  of  these  resistances  is  to  have 
A  =  9000,  B  =  900,  C  =  90  and  D  =  10  ohms,  a  total  of  10,000  ohms. 


ELECTRO-MAGNETICS. 


289 


The  current  enters  by  K  and  leaves  by  H.  The  arm  attached  to 
K  can  be  placed  on  any  desired  contact.  The  galvanometer  is 
connected  in  shunt  with  the  total  resistance  as  shown.  Let  the 
resistance  of  the  galvanometer  be  x.  With  the  arm  on  contact  1, 
let  the  total  current  be  /,  and  the  current  through  the  galvanom- 


eter be  ^    The  joint  resistance  from  K  to  H  is 


(Par-  293)- 


Hence 


Whence 


Rx 


R+x  ' 

R+x 
R 


Suppose  the  arm  to  be  placed  on  the 
resistance  from  K  to  H  is  now 


(I) 
contact.    The  joint 


R+x 

If  the  total  current  be  now  /'  and  the  current  through  the 
galvanometer  be  I'g 


. 


290 


ELEMENTS  OF  ELECTRICITY. 


Hence 


From  (I)  and  (II) 


/'  =  /'.  100. 


R  +x 


(II) 
(III) 


Or  if  D  be  the  deflection  produced  by  the  first  current  and  Df 
that  produced  by  the  second 

/'  :  7  =  100.  D'  :D 

or  the  ratio  of  the  total 

current  when  the  arm  is  on  the  T£<y  contact,  to  the  total  current 
when  the  arm  is  on  the  1  contact,  is  as  one  hundred  times  the  de- 
flection produced  in  the  first  case,  is  to  the  deflection  produced  in 
the  second  case. 

It  will  be  noted  that  x,  the  resistance  of  the  galvanometer,  does 
not  appear  in  (III),  hence  the  shunt  may  be  used  with  any  galva- 
nometer. 


B 


Fig.  170. 

382.  Weber's  Electro-Dynamometer. — This  instrument,  an  ex- 
ample of  a  galvanometer  of  the  second  class  (Par.  372),  that  is,  one 
in  which  a  coil  swings  in  a  magnetic  field  produced  by  other  coils, 
is  shown  diagrammatically  in  Fig.  170.  It  consists  of  two  large 
parallel  coils  A  and  B  mounted  so  that  they  have  a  common  axis 


ELECTRO-MAGNETICS.  291 

and  their  planes  are  vertical.  Midway  between  these  there  hangs 
by  a  bifilar  suspension  (Par.  127)  a  small  coil  C  so  arranged  that 
its  axis  is  in  the  same  horizontal  plane  but  at  right  angles  to  the 
common  axis  of  A  and  B.  As  generally  used  the  same  current 
traverses  all  three  coils.  Entering  at  E  it  flows  around  the  coil  A 
and  out  to  F,  thence  by  the  wire  to  G,  thence  down  the  slender 
wire  suspension  to  C,  around  this  coil,  up  the  other  suspension  to 
H,  down  to  D,  around  the  coil  B  and  finally  out  by  K. 

If  the  currents  in  the  two  coils  flow  as  indicated  by  the  small 
arrows,  the  field  of  AB  will  be  from  right  to  left;  that  of  C  from 
rear  to  front  and  therefore  C,  viewed  from  above,  takes  up  a  clock- 
wise motion,  or,  in  accordance  with  Maxwell's  law,  tends  to  turn 
so  that  its  field  coincides  in  direction  with  the  field  of  AB.  The 
angle  of  deflection  is  read,  as  in  the  mirror  galvanometer,  by  means 
of  a  small  mirror  attached  to  the  suspended  coil.  The  controlling 
force  is  gravity  which  tends  to  pull  the  inner  coil  back  to  its  pri- 
mary position;  the  moment  of  this  force  being  directly  proportional 
to  the  sine  of  the  angle  of  deflection,  or 

Mc  =  a .  sin  6 

The  deflecting  force  is  due  to  the  interaction  of  the  fields  of  the 
suspended  and  the  fixed  coils  and  since  these  fields  are  severally 
proportional  to  the  currents  flowing  in  the  coils  (Par.  354),  the 
deflecting  force  is  proportional  to  the  square  of  the  current.  The 
moment  of  the  deflecting  force  is  proportional  to  the  product  of 
the  square  of  the  current  and  the  cosine  of  the  angle  of  deflection, 
or 

Md  =  b .  I2 .  cos  6 

When  the  coil  conies  to  rest  the  two  moments  are  equal  and 
opposed,  hence 

6. 12. cos  5  =a. sin  6 
whence 

/2=|.tan<5 

or,  the  square  of  the  cur- 
rent is  proportional  to  the  tangent  of  the  angle  of  deflection.  This 
fact  might  have  been  anticipated  since  reflection  will  show  that 
the  instrument  is  virtually  a  tangent  galvanometer. 

In  making  an  actual  observation  a  number  of  refinements  must 
be  observed  in  determining  the  constants  a  and  b  above,  and  it 
may  also  be  necessary  to  allow  for  the  effects  of  the  earth's  field. 


292 


ELEMENTS  OF  ELECTRICITY. 


Should  the  current  through  the  instrument  be  reversed  in  direc- 
tion, the  fields  in  the  coils  will  also  be  reversed  but  from  the  figure 
it  will  be  seen  that  the  tendency  will  still  be  for  the  movable  coil 
to  turn  in  a  clockwise  direction.  Since  this  direction  of  deflection 
does  not  vary  with  reversal  of  the  current,  instruments  of  this  class, 
that  is,  two-coil  instruments,  are  employed  in  the  measurement  of 
alternating  currents,  or  those  currents  which  reverse  many  times 

per  second. 

« 

383.  Siemen's  Electro-Dynamometer. — Siemen's  electro-dyna- 
mometer, shown  diagrammatically  in  Fig.  171,  is  in  principle  the 


Fig.  171. 

same  as  Weber's  but  differs  in  that  the  movable  coil  is  external 
to  the  fixed,  and  that  the  controlling  force  is  the  torsion  of  a  deli- 
cate coiled  spring.  The  base  and  supporting  upright  are  of  wood. 
There  are  two  fixed  coils,  one  of  a  few  turns  of  heavy  wire  for  use 
with  large  currents,  the  other  of  many  turns  of  a  finer  wire  for  use 
with  smaller  currents.  The  short  coil  is  wrapped  upon  the  long 


ELECTRO-MAGNETICS.  293 

coil.  The  terminal  for  one  of  these  coils  is  the  binding  post  A,  that 
of  the  other  coil  the  binding  post  B,  and  the  remaining  end  of  each 
coil  is  connected  to  the  metal  bracket  D  which  at  one  end  carries 
a  little  cup  of  mercury.  One  terminal  of  the  movable  coil  dips 
into  this;  the  other  terminal  dips  into  a  similar  cup  just  below  the 
first,  this  last  cup  being  connected  by  a  wire  to  the  binding  post  C. 
The  movable  coil  is  suspended  either  by  a  silk  fibre  or  upon  a 
pivot  and  is  free  to  rotate  about  a  vertical  axis.  It  carries  a  needle 
or  pointer  which  is  bent  over  the  edge  of  an  upper  circular  scale. 
This  scale  may  be  graduated  in  degrees  but  more  often  in  some 
arbitrary  number  of  points,  such  as  400.  If  the  current  in  the  coils 
flow  as  indicated  by  the  arrows,  the  field  of  the  fixed  coil  is  from 
left  to  right,  that  of  the  movable  coil  from  rear  to  front  and, 
viewed  from  above,  the  rotation  of  the  movable  coil  is  counter- 
clockwise. This  movement  is  opposed  by  the  torsion  of  the  spiral 
spring  attached  to  the  upper  part  of  the  movable  coil  and  by 
means  of  a  projecting  pin  or  stop  is  restricted  to  a  few  divisions 
of  the  graduated  scale.  At  the  center  of  this  scale  there  is  a  milled 
head  to  whose  end  the  upper  end  of  the  coiled  spring  is  attached. 
Below  the  milled  head  there  is  a  second  pointer  which,  as  the  head 
is  turned,  sweeps  around  the  graduated  circle  and  indicates  the 
angle  through  which  the  head  has  been  turned. 

When  a  current  is  flowing  through  the  instrument,  the  movable 
coil  is  urged  in  a  counter-clockwise  direction.  The  milled  head  is 
turned  in  a  clockwise  direction  and  the  torsion  of  the  spiral  spring, 
which  varies  directly  as  the  angle  through  which  the  milled  head 
is  turned,  tends  to  drag  the  coil  back  to  its  primary  or  zero  position. 
When  the  coil  has  finally  been  brought  back  to  this  position,  the 
pull  exerted  by  the  spring  exactly  balances  the  contrary  moment 
exerted  by  the  current. 

Consider  a  vertical  portion  of  the  wire  in  the  movable  coil  and 
an  adjacent  portion  in  the  fixed  coil.  The  force  exerted  between 
these  portions  is  directly  proportional  to  their  length,  to  the  prod- 
ucts of  the  currents  flowing  in  them,  and  inversely  proportional 
to  the  simple  distance  between  them  (Par.  362).  The  length  of  the 
portions  is  constant,  so  also  is  the  distance  between  them,  since 
the  coil  is  always  brought  back  to  its  original  position,  therefore, 
the  force  between  the  portions,  and  consequently  the  force  be- 
tween the  coils  themselves,  varies  as  the  square  of  the  current  and 
also  as  the  number  of  divisions  of  the  scale  over  which  the  pointer 


294  ELEMENTS  OF  ELECTRICITY, 

attached  to  the  milled  head  has  been  turned.    From  this  it  follows 
that  the  current  varies  as  the  square  root  of  the  angle  of  torsion,  or 

I=KV5 

d  being  the  number  of  divi- 
sions of  the  scale  indicated  by  the  pointer.  The  constant  K  is 
different  for  different  instruments  but  is  easily  determined  by 
passing  through  the  instrument  a  known  current  /  and  noting  the 
corresponding  torsion  5. 

In  addition  to  its  use  in  measuring  currents,  this  instrument,  as 
will  be  shown  later  (Chap.  36),  may  be  used  to  measure  electrical 
power. 

384.  Ballistic  Galvanometer. — In  the  earlier  attempts  to  meas- 
ure the  velocity  of  moving  projectiles,  use  was  made  of  a  piece  of 
apparatus  called  a  ballistic  pendulum.  This  consisted  of  a  large 
pendulum  with  a  very  heavy  and  solid  bob.  The  projectile  was 
fired  against  and  embedded  itself  in  the  bob,  the  blow  causing 
the  pendulum  to  swing  through  a  certain  angle  which  was  recorded. 
Knowing  this  angle,  the  vertical  height  through  which  the  weight 
had  been  lifted  could  be  determined  and,  knowing  the  weight  of 
the  projectile,  the  velocity  with  which  it  struck  the  pendulum 
bob  could  be  calculated.  4- 

When  a  charged  body  is  discharged  through  a  conductor,  the 
charge  in  its  passage  is  a  veritable  current  but  its  duration  is  only 
momentary.  If  passed  through  a  galvanometer,  it  gives  to  the 
moving  parts  a  sudden  impulse  or  blow  comparable  to  the  blow 
given  to  the  pendulum  by  the  bullet.  If  these  moving  parts  be 
somewhat  heavy  and  therefore  rather  slow  in  vibration,  the  cur- 
rent will  have  passed  before  any  appreciable  movement  takes 
place.  It  can  be  shown  that  the  sine  of  half  of  the  angle  of  the 
first  swing  or  "throw"  of  the  needle  is  proportional  to  the  charge 
which  has  passed  through  the  coil.  (See  Gray,  Absolute  Meas- 
urements in  Electricity,  Vol.  II,  pp.  390-396.)  Galvanometers 
used  in  this  manner  are  called  ballistic  galvanometers.  They  are 
generally  of  the  suspended  coil  type  and  must  not  be  damped. 


ELECTRO-MAGNETICS.  295 


CHAPTER  31. 

ELECTRIC    MAGNETIZATION   OF   IRON   AND   STEEL. 

385.  Solenoid. — A  cylindrical  coil  of  wire  whose  length  is  great 
as  compared  to  its  diameter  is  called  a  solenoid, .the  Greek  word 
solen  meaning  a  tube.  The  successive  turns  of  the  coil  are  wrapped 
as  closely  together  as  the  thickness  of  the  insulating  covering  will 
permit  but  in  diagrams  it  is  usual,  for  the  sake  of  clearness,  to 
represent  these  turns  as  somewhat  widely  separated.  To  give  an 
accurate  shape  to  the  coil  it  is  generally  wrapped  upon  a  material 
core,  such  as  a  wooden  rod  or  a  tube  of  glass  or  paper,  which  after- 
wards may  be  withdrawn.  In  diagrams,  to  avoid  confusion  as 
to  the  direction  in  which  the  coil  is  wrapped,  it  is  preferable  to 
represent  the  core  as  in  position. 

The  coil  being  a  helix,  the  turns  are  inclined  to  the  axis  of  the 
cylinder  but  each  is  electrically  equivalent  to  a  turn  at  right  angles 


Fig.  172. 

to  the  axis  (Fig.  172)  and  a  short  portion  parallel  thereto  and  equal 
in  length  to  the  pitch  of  the  coil.  The  effect  of  these  longitudinal 
portions  is  neutralized  if  one  end  of  the  coil  be  brought  back  along 
the  axis  of  the  coil,  or  if  the  wire,  the  circular  direction  of  its  wind- 
ing being  unchanged,  be  wound  back  to  the  starting  point,  thus 
forming  a  second  layer  on  top  of  the  first. 

386.  A  Solenoid  Equivalent  to  a  Bar  Magnet. — If  a  current  be 
passed  through  a  solenoid,  application  of  the  right  hand  rule  will 
reveal  the  fact,  which  indeed  has  already  been  shown  (Par.  365), 
that  the  successive  turns  combine  in  the  production  of  a  field  in  the 
same  direction.  Thus  (Fig.  173),  all  the  lines  of  force  inside  of 
the  solenoid  run  in  the  direction  shown  by  the  long  arrow.  A 
solenoid  carrying  a  current  is  therefore  magnetically  equivalent 


296  ELEMENTS  OF  ELECTRICITY. 

to  a  bar  magnet.     It  has  poles,  it  will  attract  magnetic  sub- 
stances, it  will  attract  or  repel  the  pole  of  a  bar  magnet  and,  if 

**.  xv  VS.  y*v 


A 

nr"isr  > 

N 


\ 

Fig.  173.  \S 

freely  suspended,  it  will  turn  so  as  to  place  itself  in  the  magnetic 
meridian. 

387.  Intensity  of  Field  on  the  Axis  of  a  Solenoid.— The  inten- 
sity of  the  field  at  a  point  on  the  axis  of  a  circular  coil  is  (Par.  354) 

H   =^  dynes  (I) 

in  which  /   is  the  current  in 

absolute  units,  r  is  the  radius  of  the  coil,  and  x  is  the  slant  distance 
from  the  coil  to  the  point  on  the  axis. 

Let  P,  Fig.  174,  be  a  point  on  the  axis  of  a  solenoid  through 
which  a  current  /  is  flowing.    If  in  each  centimeter  length  of  the 

A         B 
oooooo -^  o  op.9  o  o  o  o 


oooooo  -------------------  ooooooooo 

Fig.  174. 

solenoid  there  be  N  turns,  we  may  consider  that  around  such 
unit  of  length  there  is  flowing  a  sheet  of  current  of  strength  NI. 
The  current  over  a  small  portion  AB  is  therefore  proportional  to 
the  length  of  AB  or  N.I.dl. 


Since  -  =  sin  6,  expression  (I)  can  be  written 

rj         2wlr    . 

H  =  -^-sin  0  dynes 
The  field  at  P  due  to  the  current  on  AB  is,  therefore, 


,„  ..     . 

dH=-    —  -  sin  B  (II) 


ELECTRO-MAGNETICS.  297 


From  the  figure,          =  do,  or  AE  =  AP.de  (III) 


AB  =  AP.dQ.  - 


AB  =dl= 


From  the  similar  triangles  AEB  and  BPF 
AE  :AB  =  BF  :  BP 

Hence  .  AB  =  AE  *,BP  (IV) 

or,  substituting  from  (III) 

A, 

and  as  A B  decreases,  AP  approaches  BP,  hence 

Substituting  in  (II) 

dH~2arNI.sinO.dO  (V) 

Integrating 

H  =  2wNI(—cos  0)  +  a  constant 

The  field  due  to  the  entire  solenoid  is  obtained  by  taking  this 
expression  between  the  proper  limits.  If  P  be  at  the  center  of  the 
coil  and  if  the  coil  be  so  long  that  0  =  0°  and  180°,  then 

H  =  4*rrNI  dynes 

If  P  be  at  the  mouth  of  the  solenoid  so  that  0  is  0°  and  90°, 
H=2TrNI  dynes 

or  the  field  at  the  mouth 
of  a  long  solenoid  is  one-half  what  it  is  at  the  center. 

It  is  to  be  noted  that  since  in  these  expressions  for  the  field  the 
radius  of  the  coil  does  not  occur,  the  intensity  of  the  field  would 
appear  to  be  independent  of  the  diameter  of  the  solenoid.  This, 
however,  is  not  correct  unless  the  further  condition  be  expressed, 
a  condition  already  introduced  in  the  integration,  that  the  various 
solenoids  are  geometrically  similar.  Should  the  radius  of  the 
solenoid  be  doubled  or  trebled,  its  length  must  be  likewise  doubled 
or  trebled. 

The  length  of  wire  required  in  similar  solenoids  varies  as  the 
square  of  their  like  dimensions  and  if  the  length  be  increased 
the  diameter  of  the  wire  must  be  increased  to  overcome  the  in- 
crease in  resistance,  therefore,  considerations  of  economy  lead  us 
to  make  the  coil  fit  its  core  as  closely  as  possible. 


298  ELEMENTS  OF  ELECTRICITY. 

It  has  been  shown  that  the  field  at  the  center  of  a  long  solenoid  is 
very  uniform.  If  the  solenoid  be  wrapped  upon  a  circular  core,  so 
as  to  return  upon  itself,  the  field  at  every  cross-section  is  the  same. 

388.  Ampere  Turns. — In  the  discussion  in  the  preceding  para- 
graph the  current  /  is  in  absolute  units.    If  it  be  given  in  amperes 
it  must  be  reduced  to  absolute  units  by  dividing  by  ten.    The 
expression  for  the  field  at  the  center  of  a  long  solenoid  becomes  in 
this  case  A 

H  =^.N.I  dynes 

The  field  therefore  varies  with  NI.  This  product  remains  a 
constant  if  N  and  /  vary  reciprocally,  hence  three  amperes  mak- 
ing five  turns  produce  the  same  magnetic  effect  as  five  amperes 
making  three  turns,  or  as  one  ampere  making  fifteen  turns,  or  as 
fifteen  amperes  making  one  turn.  In  any  coil  the  product  of  the 
total  number  of  turns  times  the  current  flowing  in  the  coil  is  called 
the  ampere  turns,  and  this  product  appears  as  a  factor  in  all  ex- 
pressions dealing  with  circular  coils.  We  have  already  employed 
it  in  the  discussion  of  the  tangent  galvanometer  (Par.  374). 

The  constant  4^/W  is  equal  to  1.2566  +  ;  it  is  therefore  suffi- 
ciently accurate  in  ordinary  calculations  to  say  that  H,  the  field, 
or  the  number  of  lines  of  force  per  square  centimeter  at  the  center 
of  a  long  solenoid,  is  one  and  a  quarter  times  the  ampere  turns  per 
unit  of  length. 

389.  Variation  of  Field  of  Solenoid  with  Current.— The  fact 
that  the  field  on  the  axis  of  a  solenoid  varies  directly  with  the 

S 
/N     r> ,0 


\r  r r rr\ 


Fig.  175. 


current  may  be  shown  experimentally  as  follows.  In  Fig.  175,  S 
represents  a  solenoid,  B  a  battery,  K  a  key,  R  a  rheostat  (Par. 
302),  A  an  ammeter  (a  current-measuring  instrument),  and  G  a 
galvanometer  with  a  short  needle  and  long  attached  pointers 
poised  over  a  graduated  circle  and  placed  so  that  the  axis  of  the 


ELECTRO-MAGNETICS.  299 

solenoid  prolonged  passes  through  the  pivot  of  the  needle  and  is 
perpendicular  to  the  magnetic  meridian.  By  means  of  the  rheo- 
stat, the  current  through  the  solenoid  may  be  varied  at  will.  The 
strength  of  the  current  is  read  direct  from  the  ammeter.  When 
the  key  K  is  closed,  permitting  a  current  to  flow,  the  needle  of  the 
galvanometer  is  deflected.  It  will  be  seen  that  this  is  the  case 
discussed  in  Par.  146  and  that  the  deflecting  force  (which  is  due 
to  the  field  of  the  solenoid)  varies  as  the  tangent  of  the  angle  of 
deflection.  If,  therefore,  we  lay  off  on  a  horizontal  axis  distances 
proportional  to  the  current  through  the  solenoid,  the  correspond- 
ing ordinates  laid  off  proportional  to  the  tangent  of  the  angle  of 
deflection  will  be  proportional  to  the  corresponding  field.  The 
points  so  determined  will  lie  on  a  straight  line  passing  through 
the  origin  (see  OA,  Fig.  176). 

390.  Effect  of  Material  of  Solenoid  Core  Upon  the  Field.— With 

the  apparatus  described  in  the  preceding  paragraph  we  may  in- 
vestigate the  effect  produced  upon  the  field  by  varying  the  material 
of  which  the  core  of  the  solenoid  is  composed.  Using  cores  of 
glass,  rubber,  wood,  lead,  copper,  tubes  of  various  gases  or  liquids 
or  even  vacuous  space,  no  perceptible  variation  of  the  field  is 
discovered,  its  strength  remaining  the  same  as  when  the  solenoid 
enclosed  only  air.  If,  however,  we  insert  a  core  of  steel,  the  deflec- 
tion of  the  galvanometer  needle  will  indicate  that  the  field  has 
been  increased  several  hundred  times,  that  is,  there  are  now  several 
hundred  times  more  lines  of  force  traversing  the  solenoid  than 
there  were  before  the  steel  core  was  inserted.  If  the  core  be  of 
soft  iron,  the  increase  is  still  greater;  if  it  be  of  nickel,  it  is  less  than 
in  the  case  of  steel  but  much  greater  than  in  the  case  of  air. 

391.  Permeability. — The  great  increase  in  the  density  of  the 
magnetic  flux  (number  of  magnetic  lines)  when  iron  is  inserted  in 
the  coil  has  been  explained  by  saying  that  iron  is  more  permeable, 
or  has  greater  permeability  than  the  other  substances.    When  a 
beam  of  light  falls  upon  a  sheet  of  clear  glass  many  more  rays  go 
through  than  when  the  beam  falls  upon  a  sheet  of  dark  glass.    We 
may  consider  that  in  each  case  there  is  a  force  tending  to  drive  the 
rays  through  and  that  the  dark  glass  offers  greater  resistance  while 
the  clear  glass  offers  less,  or  is  more  permeable.    So  also  there  is  a 
magnetizing  force  which  tends  to  drive  magnetic  lines  through 
the  field  of  the  solenoid.    Air,  wood,  etc.,  offer  a  magnetic  resist- 


300  ELEMENTS  OF  ELECTRICITY. 

ance  to  this  force  and  only  a  certain  number  of  lines  get  through; 
iron  and  steel  offer  much  less  resistance,  or  are  much  more  per- 
meable, and  permit  many  more  lines  to  pass.  To  this  magnetic 
resistance  the  name  reluctance  has  been  given.  It  follows  that 
reluctance  is  the  reciprocal  of  permeability  or  that  the  two  are 
comparable  to  resistance  and  conductance,  respectively. 

392.  Expression  for  Permeability. — We  have  seen  that  the  field 
of  a  solenoid  varies  directly  with  the  number  of  ampere  turns  per 
unit  of  length.    It  follows  that  the  magnetizing  force  varies  in 
the  same  manner,  hence  we  may  use  H  or  1.25  times  these  ampere 
turns  (Par.  388),  as  a  measure  of  the  magnetizing  force.    If  the 
magnetizing  force  which  produced  H  lines  per  square  centimeter 
in  air  produces  B  lines  per  square  centimeter  in  iron,  then  the  per- 
meability of  the  iron  is  Ej  H.    The  accepted  symbol  for  perme- 
ability is  the  Greek  letter  mu,  /*,  hence 

B 

M  =  H 

Hopkinson  found  that  a  magnetizing  force  which  produced  10 
lines  of  force  per  square  centimeter  in  air  produced  12,400  per 
square  centimeter  in  a  specimen  of  wrought  iron;  the  permeability 
of  the  iron  was  therefore  1,240. 

The  permeability  of  air,  glass,  and  other  non-magnetic  sub- 
stances is  unity;  that  of  bismuth,  the  most  diamagnetic  substance, 
differs  from  unity  in  the  fourth  place  of  decimals  only. 

393.  Magnetic  Saturation. — The  conception  of  permeability  as 
outlined  in  the  preceding  paragraphs  loses  some  of  its  definiteness 
when  it  is  found  that  for  magnetic  substances  it  is  not  a  constant 
but  is  different  for  different  magnetizing  forces. 

In  Par.  389  it  was  stated  that  the  field  of  a  solenoid  varies 
directly  with  the  current.  This  is  shown  by  the  line  OA  in  Fig. 
176,  in  which  the  abscissae  are  laid  off  proportional  to  the  magnet- 
izing current  and  the  ordinates  proportional  to  the  corresponding 
field.  If  we  now  insert  in  the  solenoid  a  long  soft-iron  core,  mag- 
netically neutral,  and  gradually  increase  the  current,  we  will  notice 
three  stages  in  the  field  produced:  (a)  for  small  values  of  the  cur- 
rent it  will  increase  slowly;  (b)  as  the  current  is  increased  it  will 
rise  suddenly  until  a  certain  point  is  reached,  after  which  (c)  it  will 
continue  to  increase  but  slowly.  These  stages  are  shown  graphi- 
cally in  the  curve  OD.  Since  this  curve  represents  the  field  pro- 


ELECTRO-MAGNETICS. 


301 


duced  by  the  solenoid  and  the  core  in  conjunction,  if  we  subtract 
from  its  ordinates  the  corresponding  ordinates  of  OA,  we  will  get 
the  curve  of  magnetization  of  the  core  alone.  The  result  is  the 
curve  OE.  The  upper  portion  of  this  being  very  nearly  parallel  to 

B 


A    t^'Q             *• 

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1 

1 

O 

MAG\NETIZINC\      FORCE 
Fig.  176. 

the  horizontal  axis  indicates  that  the  magnetization  of  the  core 
would  be  but  slightly  increased  by  a  further  increase  in  the 
magnetizing  current ;  in  other  words,  the  core  is  now  magnetically 
saturated. 

394.  Curves  of  Magnetization. — As  will  shortly  be  shown,  the 
designer  of  electrical  machines  and  apparatus  is  frequently  called 
upon  to  solve  problems  such  as  the  following:  Given  an  iron  core 
of  a  certain  size,  shape  and  quality;  required  the  number  of  ampere 
turns  to  produce  in  this  core  a  flux  of  a  certain  strength.  Among 
the  data  needed  for  the  solution  is  not  simply  the  permeability  of 
the  particular  kind  of  iron  of  which  the  core  is  constructed  but  its 
permeability  when  the  magnetic  flux  is  of  the  strength  called  for 
in  the  problem.  Such  information  is  contained  in  tables  but  is 
more  striking  when  presented  graphically  in  the  form  of  curves  of 
magnetization.  Fig.  177  represents  these  curves  for  five  different 
qualities  of  iron  and  steel,  whence  it  is  seen  that  soft  annealed  iron 
may  be  both  most  easily  and  most  highly  magnetized  and  that 
hard  steel  is  most  difficult  of  magnetization.  From  the  figure  it 
is  seen  that  for  a  magnetizing  force  of  5  the  magnetization  of  soft 


302 


ELEMENTS  OF  ELECTRICITY. 


iron  is  10,000,  or  the  permeability  is  2000,  while  for  a  force  of  50 
the  magnetization  is  16,000,  or  the  permeability  is  only  320. 

It  will  be  noted  that  these  curves  all  exhibit  the  three  stages  as 
described  in  Par.  393. 

•\   *NNEM-ED_IRON 
15,000 


10.000 


5.000 


10 


30     35     40      45 


Fig.  177. 


395.  Ewing's  Theory  of  Molecular  Magnetism. — The  accepted 
explanation  of  these  phenomena  is  that  advanced  by  Ewing  and 
has  already  been  given  in  part  in  Par.  153.  The  molecules  of  mag- 
netic substances  are  inherently  magnets  but  ordinarily  exhibit  no 
magnetic  effects  since  they  are  grouped  so  as  to  mutually  satisfy 
their  individual  polarities.  Application  of  a  magnetizing  force 
disturbs  this  grouping,  and  exercises  a  directive  effect  upon  the  mo- 


b  c 

Fig.  178. 

lecular  magnets,  causing  them  to  take  approximately  a  common 
direction  so  that  they  combine  in  the  production  of  a  magnetic 
flux.  His  theory,  as  the  following  will  show,  satisfactorily  ac- 
counts for  the  three  stages  in  the  curves  of  magnetization.  Let  us 
take  the  simplest  possible  hypothetical  case,  that  of  two  molecular 
magnets,  and  let  the  two  small  needles  in  a,  Fig.  178,  represent 
these  molecules.  If  they  be  remote  from  other  magnetic  bodies 


ELECTRO-MAGNETICS. 


303 


they  will  take  up  a  position  of  equilibrium  with  their  axes  lying 
upon  a  common  line.  Let  them  now,  as  shown  in  6,  be  subjected 
to  a  magnetizing  force  H.  If  H  be  feeble  the  needles  will  move 
slightly  but  will  not  swing  entirely  to  the  right  because  they  are 
pulled  back  by  their  mutual  attraction.  However,  as  H  increases, 
this  attraction  will  finally  be  overcome  and  the  needles  will  then 
whirl  suddenly  to  the  right  as  shown  in  c.  This  corresponds  to  the 
stage  of  saturation.  The  needles,  because  of  their  action  upon 
each  other,  are  not  strictly  parallel  nor  can  they  ever  become  so. 
Further  increase  of  H  can  only  pull  them  a  little  more  nearly 
parallel.  If  the  magnetizing  force  be  discontinued,  the  needles 
will  not  fly  back  at  once  to  their  original  position  but  will  linger 
and  may  require  a  slight  jar  to  cause  them  to  turn  back. 

Swing's  theory  has  been  corroborated  experimentally.  A  great 
many  small  magnetic  needles  were  distributed  side  by  side  upon 
a  long  board  which  was  then  inserted  in  a  coil  and  the  needles 
allowed  to  come  to  a  position  of  equilibrium.  The  arrangement 
was  then  subjected  to  a  gradually  increasing  magnetizing  force 
and  the  resulting  fields  were  determined  and  plotted  as  described 
above.  The  result  was  a  curve  showing  the  three  stages  of  the 
usual  magnetization  curves.  Furthermore,  when  subjected  to  a 
demagnetizing  force  the  curve  went  through  the  cyclic  changes 
described  in  the  following  paragraphs. 

396.  Hysteresis. — Suppose  that  beginning  with  a  magnetically 
neutral  specimen  of  soft  iron  and  apply- 
ing a  gradually  increasing  magnetizing 
force  we  should  determine  and  plot  the 
corresponding  curve  of  magnetization. 
Suppose  that  having  reached  a  point 
where  a  magnetizing  force  OD  (Fig.  179) 
produces  a  magnetization  DA,  we  should 
reduce  the  magnetizing  force  to  zero.  It 
will  be  found  that  the  magnetization  is 
by  no  means  reduced  to  zero  but  persists 
or  lingers  after  the  withdrawal  of  the 
force  and  has  some  such  value  as  OC. 
That  portion  of  the  curve  representing 
the  change  from  A  to  C  is  concave  to  the 


Fig.  179. 


horizontal  axis.    If  now  the  magnetizing  force  be  reapplied,  the 
curve  of  magnetization  will  not  retrace  the  path  A  NC  but  there 


304  ELEMENTS   OF  ELECTRICITY. 

will  be  a  tendency  for  the  magnetization  to  linger  at  the  value 
OC  and  it  will  increase  at  first  at  a  slower  rate  than  it  decreased, 
the  corresponding  portion  CM  A  of  the  curve  of  magnetization 
being  convex  to  the  horizontal  axis.  If  at  some  other  point  E 
the  magnetizing  force  be  again  reduced  to  zero  and  then  reapplied, 
a  similar  loop  EQ  KPE  will  be  traced,  and  so  on,  the  magnetiza- 
tion always  hold  ng  back  or  conforming  reluctantly  to  the  changes 
in  the  magnetizing  force.  To  this  phenomenon  the  term  hysteresis, 
a  lag  or  lagging,  is  applied. 

397.  Further  Data  on  Permeability. — The  magnetizing  force 
OF,  Fig.  179,  produces  the  various  degrees  of  magnetization  cor- 
responding to  FG,  FM,  FN,  FP,  FQ,  FR,  etc.    Which  of  these  is 
to  be  taken  in  determining  the  permeability  of  the  specimen?    It 
is  seen  that  the  notion  of  permeability  is  even  more  indefinite  than 
was  pointed  out  in  Par.  393,  and  that  in  order  that  it  may  be  of 
any  practical  use  we  must  know  the  previous  magnetic  history 
of  the  specimen  with  which  we  are  dealing.    It  can  easily  be  shown 
that  even  though  a  specimen  be  magnetically  neutral,  its  perme- 
ability, if  it  has  recently  been  demagnetized  by  a  single  reversal 
of  the  current,  is  very  different  from  what  it  is  if  it  has  never  been 
magnetized  at  all.     The  usual  understanding,  therefore,  is  that 
when  the  permeability  of  iron  or  steel  of  a  certain  quality  is  given, 
it  refers  to  a  specimen  which  has  not  previously  been  magnetized 
and,  furthermore,  the  permeability  has  been  determined  by  the 
application  of  a  continually  increasing  magnetizing  force  without 
reversals. 

398.  Cycle  of  Magnetization. — If  a  specimen  of  soft  iron  be 
magnetized,  then  demagnetized,  then  magnetized  to  an  equal 
degree  in  the  opposite  direction,  then  demagnetized,  and  finally 
again  subjected  to  the  original  magnetizing  force,  it  will  pass 
through  a  cycle  of  magnetization  represented  by  the  curve  in  Fig. 
180.    When  the  magnetizing  force  has  first  been  reduced  to  zero 
the  magnetization  of  the  specimen  is  still  proportional  to  OC.    In 
order  to  remove  this  residual  magnetism  an  opposite  or  negative 
magnetizing  force  OF  must  be  applied.    Since  after  the  with- 
drawal of  the  magnetizing  force  the  iron  still  retains  a  portion 
of  the  magnetism,   we  may  say  that  the  iron  clings  to  this 
magnetism  with  a  force  equal  to  the  force  OF  which  must  be 
employed  to  cause  its  relinquishment.    The  force  which  must 


ELECTRO-MAGNETICS. 


305 


be  applied  to  remove  the  residual  magnetism  is  called  the  coercive 
force. 

The  broken  curve  in  Fig.  180  represents  a  cycle  of  magnetization 
of  a  specimen  of  hard  steel,  whence  it  is  seen  that  the  coercive 


/               F 

/ 

0 

/ 

.-'"'       /'  H 

/ 

/ 

Fig.  180. 

force  is  very  much  greater  than  in  the  case  of  iron.     This  has 
already  been  shown  in  Par.  155. 

399.  Energy  Loss  Due  to  Hysteresis. — In  raising  a  weight  a 
certain  amount  of  work  must  be  performed.  If  after  the  weight 
is  raised  it  be  released,  it  will  in  its  fall  restore  the  same  amount 
of  energy.  In  magnetizing  a  bar  of  iron  or  steel  work  is  likewise 
performed  but  when  the  magnetizing  force  is  withdrawn  the  entire 
amount  of  energy  is  not  given  back,  in  other  words,  there  is  a 
loss. 

In  Par.  358  we  saw  that  the  work  expended  in  changing  the  field 
within  a  coil  carrying  a  current  is  IN  ergs,  in  which  /  is  the 
current  in  absolute  units  and  N  the  increase  or  decrease  in  the  num- 
ber of  lines  embraced.  If  there  be  n  turns  in  the  coil,  the  expres- 
sion becomes  nIN  ergs,  but  n  being  a  constant  the  work  is  always 
proportional  to  the  product  of  the  current  by  the  change  in  the 
number  of  lines  embraced. 

In  Fig.  181,  AL  is  the  average  magnetizing  force  as  the  number 
of  lines  embraced  by  the  coil  increased  from  OE  to  OF.  But  we 
have  seen  that  the  magnetizing  force  is  proportional  to  the 
current,  therefore  AL  is  proportional  to  the  current  and  the 


306 


ELEMENTS  OF  ELECTRICITY. 


H 


area  of  the  rectangle  ALxEF  is  proportional  to  IN  or  to  the 
energy  expended  while  the  magnetization  increased  from  OE 
to  OF.  In  a  like  manner  the  area  of  the  rectangle  FM  is  pro- 
portional to  the  energy  expended  while  the  magnetism  increased 
from  OF  to  0  K.  The  sum  of  these  elementary  rectangles,  or  the 
B  area  SDGO,  represents  the  total  energy  ex- 

^  pended  in  magnetizing  the  iron  to  the  stage 
OG.  It  follows  that  the  area  FDG  repre- 
sents the  energy  restored  as  the  magnetiza- 
tion falls  to  OF,  and  the  difference  between 
these  two  areas  represents  lost  energy. 
The  energy  lost  during  a  complete  cycle 
is  proportional  to  the  entire  shaded  area 
enclosed  by  the  loop.  It  will  be  seen  from 
this  that  the  lost  energy  is  much  less  in  the 
case  of  soft  iron  than  it  is  in  the  case  of 
steel.  This  lost  energy  reveals  itself  in  the 
form  of  heat,  the  temperature  of  the  core 
rising.  It  represents  waste  which  in  the 
case  of  certain  alternating-current  ma- 
chines may  assume  serious  proportions  .  It 
is  largely  on  this  account  that  the  best  and 
softest  iron  is  used  in  the  cores  of  trans- 
Fig.  18  1.  formers  (Par.  431).  Ewing  has  shown  that 

the  energy  consumed  in  subjecting  one  ton  of  soft  iron  to  100 
cycles  of  strong  magnetization  per  second  is  about  sixteen  horse- 
power and  the  energy  loss  for  a  very  hard  tungsten  steel  is  twenty 
times  greater. 

400.  Law  of  Magnetic  Circuit.—  In  Par.  387  it  was  shown  that 
the  intensity  of  the  field  at  the  center  of  an  indefinitely  long  sole- 
noid is 


in  which  N  is  the  number 

of  turns  per  centimeter  and  7  is  the  current  in  absolute  units. 
Actually  it  is  impracticable  to  employ  very  long  magnetizing  coils 
but  by  substituting  the  proper  values  in  the  integral  in  the  para- 
graph referred  to,  it  can  be  shown  that  in  applying  the  above 
formula  to  coils  whose  length  is  not  less  than  six  times  their  diam- 
eter, the  error  committed  does  not  exceed  one  per  cent.  If  the 


ELECTRO-MAGNETICS.  307 

length  of  the  magnetizing  coil  be  I  and  if  the  total  number  of  turns 
be  n,  the  above  expression  can  be  written 

ff  =  ^  ':",.;  (I) 

Suppose  this  coil  to  be  wrapped  uniformly  around  an  iron  ring 
whose  length  is  I  and  whose  permeability  is  /*.  The  flux  or  induc- 
tion per  square  centimeter  (the  word  "  induction"  being  used  in  the 
sense  of  "crop  of  lines  of  force  produced")  is 


If  the  cross-section  of  the  core  be  A,  the  total  induction  is 


This  may  be  put  in  the  following  form 


In  Par.  391  it  was  shown  that  reluctance  is  the  reciprocal  of 
permeability,  therefore  representing  1/V  by  (ft,  the  above  becomes 

(ID 


Ohm's  law  may  be  written  (Par.  285) 

E 


The  similarity  of  these  two  expressions  is  striking.  In  the  case 
of  electricity,  the  current  varies  directly  as  the  electro-motive 
force  and  inversely  as  the  resistance;  in  the  case  of  the  magnetic 
field,  the  flux  varies  directly  as  the  magneto-motive  force  and 
inversely  as  the  reluctance. 

From  (I)  47r%7,  the  magneto-motive  force,  is  equal  to  H.I  in 
which  H  is  force  in  dynes  and  I  is  length  in  centimeters,  therefore 
this  magneto-motive  force  is  measured  in  work,  or  ergs.  It  will  be 
recalled  that  the  electro-motive  force  between  two  points  is  also 
measured  (Par.  72)  by  the  work  expended  in  moving  a  unit  charge 
from  one  point  to  the  other. 


308 


ELEMENTS  OF  ELECTRICITY. 


From  (II)  it  is  seen  that,  like  resistance,  the  reluctance  varies 
directly  as  the  length  and  inversely  as  the  cross-section  of  the 
magnetized  body,  and  also  as  the  factor  (R,  which  may  be  called 
the  specific  reluctance  or  the  reluctivity  of  the  body.  It  can  be 
shown  by  the  method  used  in  Par.  288  that  specific  reluctance  is 
measured  by  the  reluctance  of  a  centimeter  cube  of  the  substance. 

The  foregoing  analogy  is  not  complete.  The  resistance  of  a 
conductor  kept  at  a  constant  temperature  does  not  vary  with  the 
current;  on  the  other  hand,  the  permeability,  and  hence  the 
reluctance,  does  vary  with  the  flux. 

401.  Calculation  of  Flux. — It  is  seldom  that  the  magnetic  cir- 
cuit is  a  complete  iron  path  as  assumed  in  the  preceding  para- 
graph. It  most  frequently  is  intersected  by  air  gaps  and  is 
composed  of  portions  which  differ  in  permeability.  In  such  a 
case  the  total  reluctance  is  the  sum  of  the  separate  reluctances 
in  series.  As  an  illustration,  suppose  we  are  required  to  calculate 

the  flux  through  a  magnetic 
circuit  as  shown  in  Fig.  182 
consisting  of  an  iron  horseshoe- 
shaped  portion  M  whose  length 
is  h,  cross-section  AI  and  per- 
meability jui,  and  a  cylindrical 
iron  armature  B,  whose  average 
length  is  4,  cross-section  A2, 
and  permeability  ju2,  the  arma- 
ture being  separated  on  either 
side  from  the  horseshoe  frame 
by  an  air  gap  of  length  4,  cross- 
section  A3  and  permeability 
unity.  The  flux,  if  /  be  in  amperes,  is 


(t 

S" 
I 

f" 

-_-.:::^QJ_:-r 

~>  \  \ 
Vi  \  \ 

1 

1 

1  1  ! 

i  i  i 

i  i  ' 

i  i 

J^  i 

'. 

. 

ill 

M 

1 

1  1  1 

1   1   1 

\ 

—ifo-  -//-  -<-ii-  H  

Jjj  - 

Fig.  182. 


A1M1  '  A2M2  ' 

As  an  alternative  problem  we  may  be  required  to  calculate  the 
ampere  turns  to  produce  a  required  flux  in  a  given  circuit.  This 
involves  the  solution  of  the  above  equation  for  nl  but  is  com- 
plicated by  the  decrease  in  permeability  with  increase  in  flux. 
The  permeability  under  the  conditions  of  the  problem  is  best 
obtained  from  tables  or  from  the  corresponding  curves  of  mag- 


ELECTRO-MAGNETICS. 


309 


netization  (Par.  394).  It  may  also  be  necessary  to  make  allow- 
ance for  a  certain  amount  of  leakage  of  flux  which  occurs  at  the 
air  gaps. 

The  foregoing  calculations  are  not  exact  but  they  enable  the 
designer  of  electrical  machinery  to  approximate  very  closely  to. 
the  solution  of  his  problems. 

402.  Diamagnetism. — In  Par.  122  reference  was  made  ta 
diamagnetism,  or  the  property  possessed  by  certain  bodies, 
notably  bismuth,  which  causes  them  to  be  feebly  repelled  from  the 
poles  of  a  magnet.  Various  attempts  have  been  made  to  account 
for  this  phenomenon,  the  explanation  now  accepted  being  based 
upon  the  theory  that  the  permeability  of  these  diamagnetic 
substances  is  less  than  that  of  the  surrounding  medium.  Fig.  183 
represents  a  block  of  bismuth  placed  in  a 
magnetic  field.  The  bismuth  being  less  per- 
meable than  the  surrounding  air,  it  crowds  off 
to  the  right  and  left  a  portion  of  the  field.  The 
tension  along  the  lines  of  force  causes  the 
bismuth  to  move  from  the  stronger  into  the 
weaker  field,  or  away  from  the  magnet. 

This  hypothesis  is  corroborated  by  the  fact 
that  a  glass  tube  filled  with  a  solution  of  an 
iron  salt  is  paramagnetic  when  suspended  in 


Fig.  183. 


air  between  the  poles  of  an  electro-magnet,  but  becomes  diamag- 
netic when  surrounded  by  a  denser  or  more  concentrated  (and 
hence  more  permeable)  solution  of  the  same  salt. 


310  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  32. 

ELECTRO-MAGNETS. 

403.  Electro-Magnets. — The  combination  of  a  coil  with  a  core 
-of  a  magnetic  substance,  usually  soft  iron,  which  is  made  a  magnet 
by  the  passage  of  a  current  through  the  coil  is  called  an  electro- 
magnet.    The  first  electro-magnets  were  made  in  1824  by  the 
English  scientist  Sturgeon.    At  that  time  insulated  wire  had  not 
been  invented  and  his  magnets  were  made  by  insulating  the  core 
by  a  thick  coating  of  varnish  and  wrapping  the  wire  on  top  of  this, 
the  successive  turns  being  so  spaced  that  they  did  not  touch  each 
other.     In  1826,  Joseph  Henry  of  Albany  discovered  how  to 
insulate  wire  by  a  silk  covering.    This  enabled  him  to  wrap  the 
wire  more  closely  and  to  put  on  several  layers  and  he  soon  pro- 
duced electro-magnets  remarkable  for  their  power.    In  1831  he 
constructed  one  whose  iron  core  weighed  less  than  sixty  pounds 
yet  could  support  over  a  ton. 

404.  Rules  for  Polarity  of  Electro -Magnets. — After  the  facts 
brought  out  in  the  preceding  chapters  it  is  perhaps  unnecessary 
to  give  a  rule  for  determining  the  polarity  of  an  electro-magnet. 
Should  such  be  needed,  the  simplest  is  the  right  hand  rule,  which 
is  merely  a  variation  of  the  rule  given  in  Par.  345.     Place  the 
palm  of  the  right  hand  upon  the  coil,  the  fingers  pointing  in  the 
direction  of  the  flow  of  the  current  (Fig.  173) ;  the  extended  thumb 
will  point  to  the  north  pole  of  the  magnet.    Another  rule  frequently 
used  is  the  following.    Face  the  pole  of  the  manget;  if  the  mag- 
netizing current  flows  around  it  in  a  clockwise  direction  it  is 
a  south  pole;   if  in  a  counter-clockwise  direction  it  is  a  north 
pole. 

405.  Value    of   Electro-Magnets. — Electro-magnets   are   used 
extensively  and  for  very  varied  purposes,  their  value  depending 
upon  the  three  following  characteristics.  j 

(1)  Their  great  power.  They  can  be  made  very  much  more 
powerful  than  the  strongest  permanent  magnets  and  they  can 
also  be  made  of  much  greater  size. 


ELECTRO-MAGNETICS.  311 

(2)  Control  of  magnetism.    The  magnetism  is  perfectly  under 
the  control  of  the  operator  and,  like  an  electric  light,  may  be 
turned  off  or  on  at  pleasure. 

(3)  Control  from  a  distance.    The  control  can  be  exerted  even 
at  distances  of  several  hundred  miles. 

406.  Tractive  Power  of  Magnets. — In  Par.  66  it  was  shown 
that  a  unit  charge  placed  near  a  plane  charged  to  a  uniform  sur- 
face density  5  is  acted  upon  by  a  force  of  2ird  dynes.  A  frequently 
employed  conception  of  magnetism  is  that  the  intensity  of 
magnetization  is  due  to  the  number  of  unit  poles  spread  over  the 
polar  or  terminal  surface  of  the  magnet  (Par.  133).  If  AT"  (Fig. 
184)  be  the  pole  of  a  bar  magnet  and  if  S  be  a  bar  of  soft  iron  or 
other  magnetic  substance  placed  so  near  N  that  all  the  lines  of 
force  which  emerge  from  N  enter  S,  then  there  will  be  as  many 


Fig.  184. 

unit  poles  upon  S  as  there  are  upon  N.  The  force  between  N 
and  S  will  be  one  of  attraction.  If  we  consider  that  the  magnetism 
upon  N  is  uniformly  distributed  and  equivalent  to  6  unit  poles 
per  square  centimeter,  then  the  same  course  of  deduction  as 
followed  in  Par.  66  will  show  that  a  unit  pole  at  P  is  attracted 
with  a  force  of  2-n-d  dynes.  If  the  sectional  area  of  AT"  be  A,  there 
are  upon  AT",  Ad  unit  poles.  There  are  an  equal  number  upon  S, 
each  of  which  is  acted  upon  by  a  force  of  2?r5  dynes,  therefore, 
the  total  attraction  between  N  and  S  is 

F  =  2<Tr5XA5=2Tr.A.52  dynes  (I) 

Since  from  each  unit  pole  there  radiate  4?r  lines  of  force  (Par. 
145),  the  total  number  per  square  centimeter  between  N  and  S 
is  H=4ir8,  whence  8  =  H/^TT. 

Substituting  in  (I)  above  we  have 

' 


or  the  tractive  force 

exerted  by  a  magnet  is  proportional  to  the  square  of  the  number  of 
lines  of  force  per  square  centimeter  of  pole  surface. 


312  ELEMENTS  OF  ELECTRICITY. 

Ewing  states  that  by  using  very  high  magnetizing  lorce  a 
magnetic  pull  of  over  225  pounds  per  square  inch  has  been 
obtained. 

A  curious  consequence  follows  from  the  above.  By  decreasing 
the  pole  area  we  increase  the  tractive  power  of  the  magnet.  This 
is  because  as  we  decrease  the  area  we  increase  the  number  of  lines 
of  force  per  square  centimeter  and  the  tractive  power  varies  as 
the  square  of  this  number.  This  is  the  explanation  of  the  fact 
referred  to  in  Par.  124,  namely,  that  if  one  end  of  a  bar  magnet 
be  square  and  the  other  end  be  rounded,  the  rounded  end  will 
exert  the  greater  pull.  The  powerful  electro-magnets  used  in 
hospitals  to  extract  particles  of  iron  from  the  eye  have  long 
conical  poles. 

The  above  expression  for  the  tractive  power  seems  to  indicate 
that  this  power  is  independent  of  the  distance  between  the  pole 
and  the  body,  but  actually  the  force  does  fall  off  very  rapidly  as 
we  recede  from  the  pole.  The  explanation  is  that  as  we  increase 
the  air  gap  we  increase  very  greatly  the  reluctance  of  the  magnetic 
circuit  and  this  in  turn  decreases  the  flux  or  H.  (Par.  401.) 

407.  Shape  of  Electro -Magnets. — Since  the  pull  of  a  magnet 
varies  as  the  square  of  the  flux  per  square  centimeter  and  since 
this  flux  varies  inversely  as  the  reluctance  of  the  magnetic  circuit, 
electro-magnets,  as  a  rule,  are  designed  so  that  the  air  gaps  in  the 
circuit  are  as  small  as  possible.    The  majority  therefore  are  either 
of  the  horseshoe  pattern  or  bent  to  three  sides  of  a  rectangle. 
The  magnetizing  coil  may  be  wrapped  over  the  whole  length  of 
the  horseshoe,  or  only  on  the  central  part  or  yoke,  but  most 
frequently  two  coils  are  used,  one  being  wrapped  on  each  leg  of 
the  core.     In  small  instruments  these  coils  are  called  spools  or 
bobbins.    The  dimensions  and  relative  proportions  of  the  parts  of 
these  magnets  are  varied  according  to  the  use  to  which  they  are 
to  be  put. 

408.  Use  of  Electro- Magnets. — The  uses  to   which  electro- 
magnets are  put  may  be  classed  under  two  general  heads;  (a)  for 
creating  the  magnetic  fields  required  for  the  operation  of  certain 
electrical  machines  and  (b)  for  exerting  a  tractive  effort  or  pull. 
The  use  for  creating  fields  will  be  described  when  the  subject  of 
electrical  machinery  is  reached.     The  second  heading  embraces 
a  most  varied  class  of  uses  among  which  are  (1)  lifting  weights. 


ELECTRO-MAGNETICS. 


313 


(2)  operating  annunciators,  call  and  alarm  bells,  etc.,  (3)  tel- 
egraphy, (4)  operating  automatic  switches,  (5)  regulating  the 
feed  of  the  carbons  of  an  arc  light,  regulating  clocks  from  a  master 
clock,  etc.  Only  a  few  of  these  can  be  described. 

409.  Lifting    Weights   by   Electro -Magnets. — Electro-magnets 
are  largely  used  in  handling  scrap  iron,  steel  billets,  boiler  plates, 
etc.    The  magnet  employed  is  shown  in  section  in  Fig.  185.    The 
core  is  a  short  and  heavy  one- 
piece  casting  consisting  of  an 

inner  cylindrical  core  sur- 
rounded by  an  annular  space 
in  which  the  magnetizing  coil 
is  wound,  the  whole  being  called 
an  iron-dad  electro-magnet. 
When  the  current  is  turned  on, 
the  inner  core  becomes  one 
pole  and  the  outer  ring  the 
other.  Owing  to  the  large 
cross-section  and  little  length 
of  the  iron  and  to  the  shortness 
of  the  air  gap  when  a  piece  of  Fig.  185. 

iron  is  in  contact  with  the  poles,  the  pull  is  very  powerful.  This 
magnet,  suspended  from  a  derrick,  is  lowered  upon  the  pile  of 
scrap  iron  that  is  to  be  moved,  the  current  is  turned  on,  the  magnet 
with  the  clinging  mass  of  iron  raised,  swung  over  to  where  it  may 
be  desired,  the  current  turned  off  and  the  iron  dropped.  In 
handling  such  objects  as  boiler  plate,  it  avoids  the  necessity  of 
using  and  adjusting  hooks,  chains  or  ropes.  The  coil  is  thoroughly 
protected  from  accidental  injury,  a  sheet  of  brass  usually  being 
inserted  in  the  annular  space. 

410.  Electric  Bells. — A  common  form  of  electric  bell  is  shown 
diagrammatically  in  Fig.  186.    It  consists  of  the  bell  or  gong  G, 
the  hammer  H,  the  electro-magnet  M,  the  battery  C  (usually 
one  or  two  dry  cells),  and  the  push  button  D.    The  hammer  is  a 
metal  knob  on  a  slender  arm  pivoted  at  P  and  bearing  at  its 
middle  the  soft  iron  armature  A.    A  delicate  spiral  spring  S  is 
attached  to  the  arm  and  exerts  upon  it  a  pull  from  the  magnet. 
At  the  back  of  the  armature  there  is  a  slender  brass  strip  which 
makes  contact  at  B  with  an  adjustable  screw.    When  the  button 


314 


ELEMENTS  OF  ELECTRICITY. 


D  is  pressed,  closing  the  circuit,  a  current  flows  from  C  to  D, 
thence  to  B,  thence  to  P,  thence  through  the  coils  of  M  and  back 
to  C.  The  cores  of  M  are  magnetized  by  this  current,  attract  the 
armature  A,  causing  the  hammer  to  strike  the  bell,  but  at  the  same 
time  break  the  circuit  at  B.  The  circuit  being  broken,  M  is  no 
longer  magnetized,  the  spring  S  pulls  the  armature  back  to  its 


Fig.  186. 

original  position,  and  the  contact  at  B  is  restored.  This  causes  the 
hammer  to  strike  the  bell  again  and  so  on,  a  rapid  succession  of 
blows  being  given  so  long  as  the  button  is  pressed.  Arrangements 
of  this  kind  for  rapidly  making  and  breaking  a  circuit  are  called 
interrupters. 

411.  The  Electric  Telegraph.— The  word  "telegraph"  meant 
originally  to  convey  messages  by  exchanging  signals  at  a  distance. 
During  the  wars  of  Napoleon  there  was  developed  a  system  of 
semaphore  signals  by  which  messages  could  be  transmitted 
rapidly  from  point  to  point.  We  read  in  the  contemporary 
accounts  of  the  campaign  in  the  Spanish  peninsula  that  Napoleon 
telegraphed  his  instructions  from  Paris  to  his  corps  commanders 
in  the  field. 

The  sending  of  signals  by  means  of  electricity  was  tried  by 
many.  An  insulated  wire  between  two  points  was  given  a  static 
charge  which  caused  a  pith  ball  at  the  far  end  of  the  wire  to  stand 
out.  If  a  charged  body  be  moved  near  the  other  end  of  the  wire 
corresponding  movements  could  be  produced  in  the  pith  ball. 


ELECTRO-MAGNETICS. 


315 


Sparks  from  a  Ley  den  jar  were  transmitted  over  a  wire  in  ac- 
cordance with  a  prearranged  code.  Use  was  made  of  the  electro- 
lytic effect  of  a  current.  Twenty-six  separate  wires,  each  marked 
to  correspond  to  a  certain  letter  of  the  alphabet,  were  stretched 
between  two  points  and  at  the  receiving  station  the  ends  of  these 
wires  dipped  into  an  acidulated  solution.  A  single  wire  led  from 
the  solution  to  the  ground.  At  the  sending  end  a  voltaic  pile  was 
used,  one  pole  of  which  was  "grounded."  When  the  other  pole 
was  touched  to  one  of  the  twenty-five  wires,  the  circuit  was  com- 
plete and  bubbles  of  gas  appeared  at  the  corresponding  end  at 
the  receiving  station.  These  various  methods  failed  mainly 
because  of  the  lack  of  a  steady  source  of  electricity.  This  difficulty 
was  overcome  by  the  invention  in  1836  of  the  Daniell  cell.  In 
the  following  year  Congress  was  induced  to  make  an  appro- 
priation of  $30,000  for  the  erection  between  Baltimore  and 
Washington  of  a  line  to  test  the  system  invented  by  Morse.  This 
proved  successful  and  with  minor  variations  is  in  operation  to-day 
over  the  greater  part  of  the  globe.  It  is  estimated  that  there  are 
now  over  five  million  miles  of  land  telegraph  lines  in  use. 

412.  The  Morse  Telegraph. — The  principle  of  the  Morse 
telegraph  will  be  readily  understood  from  the  following.  In  the 
diagram  (Fig.  187)  K  is  the  sending  and  M  the  receiving  station. 


Fig.  187. 

R  is  a  roll  of  paper  ribbon  which  is  slowly  unwound  by  clockwork 
in  the  direction  shown  by  the  arrow.  B  is  a  battery  of  Daniell 
cells,  one  pole  of  which  is  grounded  at  E.  Wh&mjhe  key  K  is 
closed  the  current  travels  from  the  battery  over^pl  line  to  the 
electro-magnet  M,  thence  to  the  ground  at  E',  thence  back 
through  the  earth  to  E.  When  M  becomes  magnetized,  the  iron 
armature  A  is  pulled  down.  This  causes  the  end  P  of  the  lever 
to  rise  and  to  press  a  pencil  against  the  moving  ribbon  at  D. 
When  the  key  K  is  opened,  the  circuit  is  broken  and  a  little 


316 


ELEMENTS  OF  ELECTRICITY. 


spring  S  pulls  the  pencil  away  from  the  ribbon.  The  length  of 
the  pencil  mark  on  the  ribbon  varies  therefore  with  the  length  of 
time  that  K  is  kept  closed  and  the  Morse  alphabet  is  accordingly 
made  up  of  a  system  of  dots,  dashes  and  intervals  or  spaces.  If 
there  be  in  the  face  of  the  drum  D  a  groove,  and  if  P  instead  of 
being  a  pencil  is  a  hard  and  smooth  stylus  which  presses  above 
this  groove,  there  will  be  produced  in  the  ribbon  long  and  short 
indentations. 

While  the  foregoing  gives  the  principle  of  the  Morse  telegraph, 
in  actual  practice  certain  conditions  arise  which  cause  a  consider- 
able modification  in  the  simple  arrangement  described  above. 
These  are  the  following: 

(1)  Each  station  must  be  able  both  to  send  and  to  receive. 

(2)  The  line  must  be  so  arranged  that  intermediate  stations 
may  be  operated. 

(3)  If  the  key  K,  Fig.  187,  be  left  open,  the  circuit  is  broken 
and  it  would  be  impossible  for  an  operator  at  M  to  send  a  signal 
to  K.    Accordingly,  in  the  American  system  the  key  K  is  kept 
closed  when  not  in  use,  in  other  words,  there  is  a  current  constantly 
flowing  over  the  line.    This  would  appear  to  be  a  wasteful  method 
and  is  avoided  in  the  European  system,  but  actually  the  current 
(and  the  consequent  waste)  is  very  small,  and  since  the  European 
system  requires  a  greater  number  of  batteries,  the  cost  is  about 
the  same. 


ear 


Fig.  188. 

(4)  It  was  soon  discovered  that  the  signals  could  be  read  by 
and   therefore   the  recording   apparatus   is   now   generally 


ELECTRO-MAGNETICS. 


317 


omitted  and  in  its  place  is  substituted  a  sounder,  an  instrument 
shown  in  simplest  form  in  Fig.  188.  A  horizontal  brass  lever  L, 
pivoted  at  P,  is  pulled  down  at  one  end  by  the  spring  S  until  the 
other  end  is  pressed  up  against  the  adjustable  contact  B.  The 
lever  carries  on  its  upper  side  the  crosswise  soft  iron  armature  A 
and  below  this  armature  is  the  electro-magnet  M.  When  a  current 
flows  through  M  the  core  is  magnetized,  A  is  attracted  and  the 
lever  is  pulled  down  until  the  contact  D  strikes  the  brass  frame 
just  below,  making  a  loud  click.  When  the  current  is  broken  the 
spring  S  causes  the  lever  to  fly  up  and  strike  B,  making  a  second 
click.  The  interval  between  these  successive  clicks  determines 
whether  the  sound  be  a  dot  or  a  dash. 

(5)  The  currents  employed  are  only  a  few  thousandths  of  an 
ampere  (not  entirely  through  choice  but  because  of  the  resistance 


Fig.  189. 

of  the  line),  and  are  usually  not  strong  enough  to  actuate  directly 
either  the  recording  device  or  the  sounder.  Morse  overcame  this 
difficulty  by  means  of  a  relay,  an  electro-magnet  so  placed  in  the 
main  circuit  that  when  a  current  flowed  the  magnet  attracted 
an  armature  which  in  its  movement  closed  an  auxiliary  circuit, 
thereby  throwing  in  a  local  battery  which  supplied  the  necessary 
current  to  operate  the  recording  apparatus.  This  arrangement 
is  shown  diagrammatically  in  Fig.  189  in  which  M  is  the  electro- 
magnet in  the  main  line  LL,  A  is  the  armature,  hinged  at  P  and 
drawn  up  against  the  adjustable  stop  K  by  the  feeble  tension  of 
the  spring  S.  When  a  current  passes  through  M ,  the  armature  A 


318 


ELEMENTS  OF  ELECTRICITY. 


is  attracted  and  makes  contact  at  C,  thus  throwing  in  on  the 
sounder  the  auxiliary  battery  B.  The  armature  is  therefore 
really  a  switch  or  key  for  the  local  circuit. 

413.  The  American  System. — The  operation  of  the  American 
system  will  be  understood  from  Fig.  190.  The  operator  in  Boston, 
preparatory  to  signalling,  opens  the  switch  S  of  his  sender.  This 


Fig.  190. 

breaks  the  circuit  and  stops  the  current  in  the  line.  When  he 
closes  his  key  K,  the  circuit  is  restored,  a  current  flows,  each  of 
the  electro-magnets  pulls  down  its  relay  armature  thus  causing 
every  sounder  to  click.  A  signal  made  at  one  station  is  therefore 
repeated  at  every  station  on  the  line.  Should  the  New  York 
operator  wish  to  interrupt,  he  opens  his  switch  S,  thus  break- 
ing the  circuit.  The  Boston  operator  is  aware  of  this  at  once 
because  his  own  sounder  ceases  to  click,  and  he  at  once  closes 
his  switch  and  awaits  instructions  from  New  York.  Whenever 
a  message  is  completed,  the  operator  must  at  once  close  his 
switch. 

Should  a  break  occur  in  a  line,  it  is  still  possible  to  use  the 
remainder.  Thus,  should  a  break  occur  between  Providence  and 
Boston,  the  Providence  operator  by  grounding  his  line,  as  shown 
by  the  dotted  line,  restores  communication  with  New  York. 
Should  the  break  be  between  Providence  and  New  York,  he  must 
ground  his  line  to  the  right  of  his  key. 


ELECTRO-MAGNETICS. 


319 


414.  Overload  Switch. — Should  a  short  circuit  occur  on  an 
electric-lighting  or  on  a  power  circuit,  serious  injury  may  result. 
Various  automatic  devices  are  employed  to  afford  protection  in 
such  cases.    We  saw  in  Par.  306  the  use  of  fuses  for  this  purpose. 
There  have  been  devised  many  kinds  of  switches  which  auto-, 
matically  break  the  circuit  when  the  current  exceeds  a  certain 
maximum  for  which  they  are  set.    These  are  called  circuit-breakers 
or  overload  switches,  the  word  "load"  in  electric  parlance  meaning 
current.    They  are  therefore  analogous  to  safety  valves. 

One  of  these  is  shown  diagrammatically  in  Fig.  191.  The 
switch  A  when  closed  makes 
contact  through  a  curved  arm 
with  two  points  B  and  C.  A 
stout  spring,  S,  tends  to  throw 
the  switch  in  the  direction 
shown  by  the  arrow  but  is 
prevented  from  doing  so  by  a 
hook  H  which  engages  in  a 
corresponding  hook  on  the  trig- 
ger T.  The  current  enters  at 
E,  passes  thence  to  B,  thence 
through  the  switch  to  C,  thence 
around  the  coil  G  and  out  by  F. 
Within  the  coil  G  there  is  a 
soft  iron  core.  As  the  current 
increases  in  strength,  the  coil 
exerts  a  greater  and  greater 
pull  upon  this  core  until  finally 
it  is  lifted  bodily.  As  it  moves 
upward  it  strikes  the  trigger  T, 
releasing  the  switch  which  is 
then  thrown  forcibly  up,  thus 
breaking  the  circuit.  The  Fig.  191. 

farther  the  core  is  inserted  in  the  coil,  the  more  easily  it  is  lifted, 
therefore,  by  means  of  the  screw  K,  the  switch  may  be  set  to  trip 
at  any  desired  limit. 

415.  Underload  Switch. — Automatic  switches  are  also  in  use 
which  trip  when  the  current  falls  below  a  certain  minimum.    One 
form  is  shown  diagrammatically  in  Fig.  192.    An  arm,  pivoted  at 
P,  carries  at  one  end  a  weight  W  and  at  the  other  end  an  arc  of 


320 


ELEMENTS  OF  ELECTRICITY. 


wire  whose  extremities  dip  into  mercury  cups.  The  current,  flow- 
ing as  shown,  passes  around  M,  thence  to  the  first  mercury  cup, 
thence  across  the  arc  to  the  second  cup  and  out.  The  armature  A 
is  attracted  and  held  by  the  electro-magnet  M.  When  the  current 
decreases  below  a  certain  point,  M  can  no  longer  hold  A,  the 
weight  W  falls  and  lifts  the  ends  of  the  arc  out  of  the  mercury 

cups,  thus  break- 
ing the  circuit. 
Instead  of  these 
"mercury  break" 
switches,  prefer- 
ence is  now  given 
to  forms  similar 
to  the  overload 
switch,  described 
in  the  preceding 


Fig.  192. 


paragraph,  the  switch  being  thrown  open  by  a  compressed  spring 
when  the  current  falls  below  a  certain  minimum. 

At  first  sight  it  is  not  clear  why  an  underload  switch  is  needed. 
The  following  is  an  example  of  its  use.  Fig.  193  represents  a 
storage  battery  B  being  charged  by  current  from  a  generator  G 
through  an  underload  switch  S.  It  was  shown  in  Par.  245  that 
in  order  to  drive  a  current  through  the  battery,  the  E.  M.  F.  of 
the  generator  should  be  about  ten  per  cent  greater  than  that  of 
the  battery.  Suppose  that  by  some  accident  during  the  charging, 


Fig.  193. 

such  as  the  belt  slipping,  the  generator  should  slow  down  or 
should  stop.  The  moment  the  E.  M.  F.  of  the  generator  falls 
below  that  of  the  battery,  the  battery  would  at  once  begin  to 
discharge  back,  and  the  resistance  of  the  generator  being  very 
small,  the  discharge  would  amount  to  a  short  circuit.  However, 
before  a  current  can  be  reversed  it  must  die  down  and  pass  through 
zero,  therefore,  before  the  battery  could  discharge,  the  underload 
switch  would  trip  and  thus  protect  it. 


ELECTRO-MAGNETICS. 


321 


CHAPTER  33. 

INDUCTION. 

416.  Faraday's  Discovery  of  Induction. — In  Fig.  194,  C  is  a 
hollow  cylindrical  coil  of  wire  connected  in  circuit  with  a  galva- 
nometer G,  and  M  is  a  magnet  held  above  the  coil.  If  the  magnet 


Fig.  194. 

be  quickly  thrust  into  the  coil,  the  galvanometer  needle  will  be 
deflected  indicating  a  current  in  (7,  but  the  deflection  is  only 
momentary  and  if  the  magnet  after  insertion  be  held  motionless, 
the  needle  will  at  once  return  to  its  zero  position.  If,  after  the 
needle  has  come  to  rest,  the  magnet  be  quickly  withdrawn  from 
the  coil,  the  galvanometer  will  again  indicate  a  momentary 
current  but  in  this  case  in  a  direction  opposite  to  that  produced  by 
the  insertion  of  the  magnet.  The  more  rapidly  the  magnet  is 
inserted  or  withdrawn,  the  greater  the  momentary  current  as 
indicated  by  the  greater  deflection  of  the  galvanometer  needle. 
If  the  magnet  be  reversed  end  for  end,  the  currents  will  likewise 
be  reversed.  Finally,  if  the  magnet  be  held  motionless  and  the 


322 


ELEMENTS  OF  ELECTRICITY. 


coil  be  moved,  the  same  results  are  obtained,  that  is,  the  motion 
of  the  magnet  and  coil  need  only  be  relative. 

These  facts  were  discovered  by  Faraday  in  1831.  Their 
importance  can  hardly  be  overestimated  since  they  are  the  basis 
of  nine-tenths  of  the  present  commercial  production  of  electricity. 
The  currents  produced  in  the  coil  by  these  movements  are  said 
to  be  induced  and  the  phenomenon  is  called  induction. 

If  there  be  a  break  in  the  circuit  of  the  coil  there  will  be  an 
induced  E.  M.  F.  but  no  current,  and,  to  avoid  repetition,  it  is 
to  be  borne  in  mind  hereafter  that  whenever  reference  is  made  to 
induced  E.  M.  F.  there  will  also  be  an  induced  current  in  the  same 
direction,  provided  the  circuit  be  complete. 

We  have  already  seen  (Par.  403)  how  a  magnet  may  be  pro- 
duced by  the  electric  current;  the  above  shows  the  reverse  proc- 
ess, the  production  of  an  electric  current  by  means  of  a  magnet. 
It  must,  however,  be  noted  that  in  the  production  of  a  magnet  by 
means  of  a  current  there  is  an  expenditure  of  electrical  energy, 
while  in  the  production  of  a  current  by  means  of  a  magnet  there 
is  no  loss  of  magnetism  and  the  magnet  suffers  no  diminution  in 
strength.  More  physical  energy  is  required  to  move  the  magnet 
or  the  coil  relative  to  each  other  than  is  required  if  a  soft  iron 
bar  of  equal  weight  be  substituted  for  the  magnet,  and  this  extra 
energy  is  the  source  of  the  electrical  energy. 

417.  Faraday's  Second  Discovery. — Since  inserting  into  the 
coil  an  unmagnetized  bar  of  iron  or  steel,  otherwise  exactly  similar 


Fig.  195. 


to  the  magnet,  produces  no  effect,  it  follows  that  the  current  must 
have  been  produced,  not  by  the  movement  of  the  magnet  alone 
but  by  the  movement  of  the  field  surrounding  the  magnet.  Since 
this  field  consists  of  space  traversed  by  lines  of  force,  we  may  state 
that  if  lines  of  force  are  thrust  into  or  withdrawn  from  a  circuit, 
an  E.  M.  F.  is  induced  in  the  circuit.  It  is  not  necessary  that  the 


ELECTRO-MAGNETICS.  323 

magnet  be  actually  inserted  in  the  coil  provided  it  be  so  moved  as 
to  alter  the  number  of  lines  of  force  traversing  the  coil.  It  follows 
logically  from  the  foregoing  that  induced  currents  may  be  pro- 
duced by  using  lines  of  force  produced  otherwise  than  by  magnets, 
that  is,  by  currents. 

In  Fig.  195  B  represents  a  battery,  P  a  coil  of  wire  and  S  a. 
second  coil  near  to  the  first  and  connected  to  the  galvanometer  G. 
There  is  no  electrical  connection  between  P  and  S.  With  K 
closed  and  a  current  flowing  in  P,  the  galvanometer  will  indicate 
a  momentary  induced  current  in  S  if  P  be  moved  nearer  to  S,  and 
a  momentary  current  in  the  opposite  direction  if  P  be  moved 
farther  from  S.  This  production  of  an  induced  current  by  vary- 
ing the  position  of  a  current  with  reference  to  a  circuit  was  the 
second  of  Faraday's  discoveries  in  induction.  To  the  coil  P  he 
applied  the  name  primary,  and  to  the  coil  S,  the  one  in  which  the 
current  is  induced,  the  name  secondary. 

Without  varying  the  position  of  P  and  S,  a  momentary  current 
is  induced  in  S  whenever  K  is  closed,  and  one  in  the  opposite 
direction  when  K  is  opened.  These  are  but  extreme  cases  of  the 
general  case  above,  for  to  close  the  key  is  equivalent  to  bringing 
up  a  current  to  P  from  an  infinite  distance,  and  to  open  the 
key  is  equivalent  to  removing  the  current  in  P  to  an  infinite 
distance. 

In  the  case  of  the  magnet,  induction  took  place  only  while  the 
magnet  was  moving;  so  in  this  case  induction  takes  place  only 
while  the  current  in  the  primary  is  changing,  or  while  the  primary 
with  current  flowing  is  being  shifted  in  position  relative  to  the 
secondary. 

418.  Inertia  of  Electro -Magnetic  Fields. — A  physical  explana- 
tion of  induction  may  be  given  if  the  following  preliminary  con- 
ceptions be  grasped. 

(a)  The  space  embraced  by  an  electric  circuit  is  at  any  given 
time  pervaded  by  n  lines  of  force.    If  the  convention  be  adopted 
that  lines  in  one  direction  are  positive,  then  those  in  the  opposite 
direction  must  be  considered  negative  and  therefore  n  may  have 
any  value,  positive,  or  negative,  or  zero. 

(b)  Positive  and  negative  lines  of  force  neutralize  each  other,  in 
other  words,  a  sufficient  number  of  lines  of  force  of  one  kind  may 
be  introduced  into  a  field  of  the  opposite  kind  to  weaken  the  field, 
or  to  reduce  it  to  zero,  or  to  reverse  it. 


324 


ELEMENTS  OF  ELECTRICITY. 


(c)  Electro-magnetic  fields  possess  a  property  which  has  been 
termed  electro-magnetic  inertia  and  which  is  analogous  to  the 
inertia  of  matter.  Inertia  is  a  property  of  matter  by  which  the 
matter  resists  any  change  of  its  state  with  respect  to  rest  or  motion. 
Thus,  a  body  at  rest  resists  being  put  in  motion  and  a  body  in 
motion  resists  being  accelerated,  retarded,  turned  aside,  or  stop- 
ped. This  resistance  manifests  itself  only  so  long  as  the  change 
in  the  state  of  the  body  is  being  made  and  disappears  the  instant 
the  change  is  accomplished.  Electro-magnetic  inertia  may  be 
said  to  be  the  property  by  which  electro-magnetic  fields  resist  any 
change  in  the  number  or  direction  of  their  lines  of  force.  This 
resistance  manifests  itself  as  E.  M.  F.  and  corresponding  current 
in  the  circuit,  which  current  tends  to  produce  lines  of  force  of  such 
number  and  kind  as  to  keep  the  original  number  constant.  Like 
the  inertia  of  mass,  it  reveals  itself  only  while  the  change  in  the 
number  of  lines  in  the  field  is  taking  place  and  vanishes  as  soon 
as  the  change  has  taken  place. 

419.  Explanation  Applied  to  Magnet  and  Coil. — To  illustrate, 
consider  the  case  of  the  magnet  and  the  hollow  coil  (Fig.  196). 


Fig.  196. 


At  the  outset,  the  number  of  lines  in  the  field  of  the  coil  may  be 
considered  zero.  If  we  thrust  in  the  magnet  in  the  direction  shown 
in  the  figure,  we  push  in  lines  of  force  from  above  downward. 


ELECTRO-MAGNETICS. 


325 


The  current  induced  in  the  coil  is  in  such  direction  as  to  produce 
lines  of  force  upward,  that  is,  tending  to  neutralize  those  which 
are  being  inserted  and  thus  keeping  the  original  number  in  the 
field  unvaried.  Applying  the  right  hand  rule  (Par.  404),  we  see 
that,  looking  down  into  the  coil  from  above,  the  induced  current 
will  be  counter-clockwise. 

Had  the  magnet  been  reversed  and  the  south  pole  been  inserted 
in  the  coil,  the  lines  of  force  would  have  been  thrust  in  in  a  nega- 
tive direction,  or  pointing  upwards,  which  must  be  considered  as  a 
decrease  in  the  number  in  the  original  field.  The  induced  current 
would  therefore  have  been  in  such  direction  as  to  send  lines  of 
force  downward,  that  is,  viewed  from  above,  it  must  have  been 
clockwise. 

Upon  withdrawing  the  magnet  in  the  first  case,  we  decrease  the 
number  of  lines  embraced  by  the  coil.  The  induced  current  is  in 
such  direction  as  to  compensate  for  this  withdrawal  by  producing 
lines  running  downward,  hence,  looking  at  the  coil  from  above, 
the  current  is  clockwise. 

Similarly,  withdrawing  the  magnet  which  had  been  inserted 
south  end  foremost  produces  a  counter-clockwise  induced  current. 

420.  Explanation  Applied  to  Two  Coils. — Consider  the  case  of 
the  two  coils  as  described  in  Par.  417.  Upon  closing  the  key  (Fig. 
197)  the  current  flows  around  P  as  indicated.  This  produces  in 


Fig.  197. 


the  coil  P  lines  of  force  in  the  direction  shown  by  the  large  arrow, 
and  as  the  two  coils  are  now  placed,  some  of  these  lines  pass 
through  S  thus  changing  the  number  of  lines  in  the  latter's  field. 
The  current  induced  in  S  is  in  such  direction  as  to  produce  lines  of 
force  opposed  to  those  coming  from  P.  This  current,  viewed  from 
P,  is  therefore  counter-clockwise. 

Similarly,  when  K  is  opened  the  effect  is  to  withdraw  these 
lines  of  force  from  S  and  the  current  induced  in  S  is  in  direction  to 


326 


ELEMENTS  OF  ELECTRICITY. 


produce  others  to  replace  those  being  withdrawn,  hence,  seen  from 
P,  the  current  is  clockwise. 

With  the  current  flowing  in  P,  changes  in  the  position  of  P  with 
respect  to  S  vary  the  number  of  lines  through  S  and  induce  cur- 
rents in  S  in  accordance  with  the  principles  just  given. 

421.  Rule  for  Direction  of  Induced  E.  M.  F. — A  simple  rule  for 
remembering  the  direction  of  the  induced  E.  M.  F.  (and  current) 
in  a  coil  is  the  following.    Look  through  the  coil  in  the  positive  direc- 
tion of  the  lines  of  force;  a  decrease  in  the  number  enclosed  induces  a 
clockwise  E.  M.  F.;  an  increase  induces  a  counter-clockwise  E.  M.  F. 

422.  Right  Hand  Rule  for  Direction  of  Induced  E.  M.  F.— There 
are  certain  cases  where  the  beginner  may  be  perplexed  as  to  the 
application  of  the  foregoing  rule.     Thus,  the  conductor  under 


consideration  may  not  form  a  coil  but  may  be  a  straight  piece  of 
wire,  or  there  may  be  a  coil  but  its  position  may  be  in  doubt,  only 
a  portion  of  it  being  visible.  For  example,  the  coils  on  the  arma- 
ture of  a  dynamo  are  often  interwoven  in  an  intricate  manner  and 
further  concealed  by  a  covering  of  insulating  material,  yet  it  may 
be  necessary  to  determine  the  direction  of  the  induced  E.  M.  F. 


ELECTRO-MAGNETICS. 


327 


In  such  cases  the  following  right  hand  rule  seems  to  be  the  sim- 
plest. Place  the  right  hand  upon  the  conductor,  the  thumb  point- 
ing in  the  direction  of  its  motion,  the  palm  turned  to  receive  the  lines 
of  force  of  the  field;  the  extended  fingers  will  indicate  the  direction  of 
the  induced  E.  M.  F. 

In  Fig.  198  the  conductor  AB  is  moving  upward  and  the  direc- 
tion of  the  induced  E.  M.  F.  is  from  A  to  B. 


These  two  rules  are  of  course  perfectly  compatible.  For  ex- 
ample, suppose  AB  (Fig.  199)  to  be  a  part  of  either  the  coil  ABC 
or  of  the  coil  ABD.  If  it  be  ABC,  the  upward  movement  will 
carry  it  out  of  the  field,  there  will  be  a  decrease  in  the  number  of 
lines  embraced  and  the  induced  E.  M.  F.  will  be  clockwise,  or  from 
A  to  B.  If  it  be  ABD,  the  upward  movement  will  carry  it  into 
the  field,  there  will  be  an  increase  in  the  number  of  lines  embraced 
and  the  induced  E.  M.  F.  will  be  counter-clockwise,  or  again  from 
A  to  B. 

If  the  plane  of  the  coil  be  moved  parallel  to  the  lines  of  force, 
or  if  the  coil  be  moved  parallel  to  itself  in  a  uniform  field,  there  is 
no  increase  or  decrease  in  the  number  of  lines  embraced  and  con- 
sequently no  induced  E.  M.  F.  This  same  conclusion  may  be 


328  ELEMENTS  OF  ELECTRICITY. 

derived  from  Par.  358.  To  induce  E.  M.  F.  there  must  be  an  ex- 
penditure of  energy,  but  since  the  number  of  lines  embraced  by 
the  coil  is  unaltered,  there  is  no  such  expenditure.  From  another 
point  of  view  it  may  be  considered  that  in  each  half  of  the  coil 
there  is  induced  an  equal  E.  M.  F.  but  these  being  in  opposite 
directions,  the  resultant  E.  M.  F.  is  zero. 

423.  Mechanical   Production  of  Electric   Current. — Since  the 
insertion  of  a  magnet  into  a  coil  induces  a  momentary  current  and 
the  withdrawal  of  the  magnet  induces  a  momentary  current  in 
the  opposite  direction,  it  is  possible  to  construct  a  machine  by 
which  a  reciprocating  motion  is  given  to  a  magnet  which  alter- 
nately enters  and  recedes  from  a  coil  and  thus  induces  an  alternat- 
ing current  in  the  coil  and  in  its  circuit.    Such  a  machine  would  be 
of  low  efficiency.    But  we  have  also  seen  (Par.  417)  that  it  is  not 
necessary  to  actually  insert  the  magnet  into  the  coil  provided  it 
be  so  moved  as  to  vary  the  number  of  lines  of  force  through  the 
coil.    For  example,  it  could  be  swept  across  the  mouth  of  the  coil. 
This  is  the  basis  of  the  construction  of  modern  machines  for  gen- 
erating electric  current.    A  number  of  coils  are  fixed  radially  upon 
the  outer  circumference  of  a  circle  which  rotates  within  a  larger 
circle  upon  whose  inner  circumference  are  attached  magnets,  or 
they  may  interchange  places  and  the  magnets  may  rotate  and  the 
coils  remain  fixed.    As  the  coils  and  the  magnets  sweep  by  each 
other  at  high  speed,  alternating  currents  are  induced  in  the  coils 
and  are  drawn  off  and  utilized.    Such  machines  are  called  gener- 
ators and  are  explained  in  detail  later  on. 

424.  Cutting  Lines  of  Force. — Electro-motive  force  is  induced 
by  varying  the  number  of  lines  of  force  embraced  by  a  circuit.    A 
line  of  force  is  a  closed  curve.    A  circuit  is  also  a  closed  figure. 
Therefore,  like  two  links  of  a  chain,  in  order  that  a  line  of  force 
may  be  inserted  into  or  withdrawn  from  a  circuit,  one  or  the  other 
must  be  cut  and  it  is  usually  the  line  of  force.    Hence,  on  account 
of  the  conciseness  of  the  expression,  it  is  convenient  and  custom- 
ary to  speak  of  the  E.  M.  F.  generated  by  "cutting  lines  of  force." 
It  must,  however,  be  remembered  that,  as  was  shown  in  Par.  422, 
in  speaking  thus  we  mean  by  the  number  cut  the  number  by  which 
the  original  field  embraced  by  the  circuit  has  been  increased  or 
decreased,  for  when  a  circuit  is  moved  parallel  to  itself  across  a 
uniform  field,  there  are  certainly  lines  cut,  but  since  the  original 
number  embraced  is  unvaried,  there  is  no  E.  M.  F.  induced. 


ELECTRO-MAGNETICS.  329 

425.  Relation  Between  Rate  of  Cutting  of  Lines  of  Force  and 
the  Resulting  E.  M.  F. — In  Par.  416  it  was  shown  that  the  more 
rapidly  the  field  embraced  by  the  coil  is  varied,  the  greater  is  the 
induced  E.  M.  F.  The  relation  between  the  induced  E.  M.  F.  and 
the  rate  of  cutting  of  lines  of  force  may  be  deduced  as  follows. 


Fig.  200. 

Let  EG  and  DF,  Fig.  200,  represent  two  parallel  metal  rails  con- 
nected across  DE  and  embracing  between  them  a  uniform  field 
whose  positive  direction  is  upward.  Let  AB  be  a  wire  resting 
across  these  rails.  If  this  wire  be  slid  along  towards  DE,  there 
will  be  induced  a  current  I  which  will  flow  around  the  enclosed 
rectangle  in  the  direction  ABED.  If  the  movement  of  the  wire 
and  the  resulting  flow  of  current  continue  for  a  time  dt,  the  total 
quantity  of  electricity  which  is  moved  around  the  circuit  is 
Q  =  I.dt,  whence  /  =Q/dt.  If  during  this  time  the  number  of  lines 
of  force  embraced  by  the  rectangle  be  decreased  by  d  N,  the  work 
done  (which  has  resulted  in  moving  these  Q  units  around  the  cir- 
cuit) is  (Par.  358)  W  =  I.dN. 

Substituting  in  this  the  expression  for  /  above,  we  have 


The  E.  M.  F.  induced  in  the  circuit  being  E,  if  the  circuit  be  cut 
at  any  point  there  will  be  a  difference  of  potential  E  between  the 
opposite  sides  of  the  resulting  gap.  In  Par.  72  it  was  shown  that 
the  difference  of  potential  between  two  points  is  measured  by  the 
work  expended  in  moving  a  unit  quantity  of  electricity  from  one 
point  to  the  other.  Since,  from  the  above,  it  required  an  expendi- 
ture of  Q  .  d  N/dt  ergs  to  move  Q  units  through  this  difference  of 
potential,  to  move  one  unit  requires  dN  /dt  ergs,  hence 

F       dN 
E='-~dt 

or  the  induced  E.  M.  F.  varies 
directly  with  the  rate  of  cutting  of  the  lines  of  force. 


330  ELEMENTS  OF  ELECTRICITY. 

Had  the  coil  consisted  of  n  turns,  the  work  done  would  have  been 
W=Q.n.dN/dt  (Par.  358)  and  hence 

dN 
E  =  n'-dt 

or  the  induced  E.  M.  F.  also 
varies  directly  with  the  number  of  turns  in  the  coil. 

It  is  a  simple  matter  to  confirm  experimentally  the  foregoing 
conclusions. 

426.  Absolute  Electro  -Magnetic  Unit  of  E.  M.  F.—  If  a  coil 
embraces  N'  lines  of  force  and  after  an  interval  t  embraces  N", 
the  average  E.  M.  F.  generated  is 


., 

If  Nf  —  N"  be  positive,  there  has  been  a  decrease  in  the  number 
of  lines  embraced  and  the  induced  E.  M.  F.  is  positive  or  clockwise. 
If  it  be  negative,  the  induced  E.  M.  F.  is  negative  or  counter-clock- 
wise. 

If  in  the  above  expression  N'  —  N"  be  unity  and  t  be  one 
second,  E  becomes  unity,  whence  the  absolute  electro-magnetic 
unit  of  E.  M.  F.  is  defined  as  that  E.  M.  F.  induced  by  cutting  one 
line  of  force  per  second. 

427.  The  Practical  Unit  of  E.  M.  P.,  the  Volt.—  The  absolute 
unit  of  E.  M.  F.  is  entirely  too  small  for  practical  purposes,  and 
even  a  unit  corresponding  to  the  E.  M.  F.  produced  by  the  cutting 
of  one  million  lines  per  second  is  extremely  small.  In  deciding 
upon  a  practical  unit,  the  Paris  Congress  of  Electricians  in  1881 
might  have  taken  the  E.  M.  F.  produced  by  cutting  one  million, 
or  ten  million,  or  one  hundred  million,  or  even  one  billion  lines  of 
force  per  second,  but  in  this  selection  they  were  probably  guided 
by  the  following  considerations.  Before  the  adoption  of  a  unit  of 

E.  M.  F,,  the  need  for  such  a  unit  had  been  felt  and  it  was  quite  the 
custom  to  take  as  an  every-day  standard  of  comparison  the  E.  M. 

F.  of  a  Daniell  cell,  the  most  constant  cell  then  in  general  use. 
In  the  older  books  we  frequently  find  E.  M.  F.  specified  in  terms 
of  that  of  so  many  Daniell  cells.    To  disturb  these  conceptions 
as  little  as  possible,  the  practical  unit  was  selected  as  that  one 
which  most  nearly  approximated  to  the  E.  M.  F.  of  a  Daniell 
cell.    The  practical  unit  of  electro-motive  force,  the  volt,  is  there- 


ELECTRO-MAGNETICS. 


331 


fore  defined  as  the  E.  M.  F.  produced  by  cutting  one  hundred  million 
(108)  lines  of  force  per  second.  The  volt  is  therefore  equal  to  108 
absolute  units  of  E.  M.  F.  The  average  E.  M.  F.  of  a  Daniell 
cell  is  1.07  volt  (Par.  206). 

If  in  Ohm's  law,  I  =  E/R,  we  substitute  for  I  its  value  in 
absolute  units  /XlO-1,  and  for  E  its  value  #Xl08,  we  see  that 
for  R  we  must  put  R  XlO9,  therefore,  the  ohm  is  109  absolute  units 
of  resistance. 

428.  Eddy  Currents. — In  the  preceding  paragraphs  'we  have 
considered  currents  induced  in  coils  when  the  flux  embraced  by 
the  coils  is  varied.  The  phenomenon  of  induction  is  still  more 
general  and  whatever  the  shape  of  a  conductor,  that  is,  whether  it 
be  a  sphere,  or  a  plate,  or  an  irregular  lump,  currents  are  induced 
in  it  whenever  there  is  an  increase  or  decrease  in  the  number  of 
lines  of  force  penetrating  the  body. 

In  1824  Gambey  observed  that  a  compass  needle  set  to  oscillat- 
ing above  a  sheet  of  copper  came  to  rest  much  more  quickly  than 
when  placed  above  a  wooden  board.  This  observation  was  in- 
vestigated by  Arago  who  made  the  additional  discovery  that  a 
disc  of  copper  rotated  either  above  or  below  a  needle  produces  a 
deflection  of  the  needle  in  the  direction  of  the  rotation,  and  if 
rotated  rapidly  enough  would  cause  the  needle  also  to  take  up  a 
motion  of  rotation.  This  experiment  is  noteworthy  since  the 
endeavor  to  account  for  the  movement  of  the  needle  led  Faraday 
to  the  discovery  of  induction  as  outlined  in  paragraphs  416  and 
417  above. 


Fig.  201. 

The  movement  of  the  needle  may  be  explained  as  follows:  NS, 
Fig.  201,  represents  a  needle  suspended  above  a  copper  disc  which 
latter  is  caused  to  rotate  in  a  clockwise  direction.  Consider  at 
any  one  instant  a  strip  AB  along  the  diameter  of  the  disc  and 


332  ELEMENTS  OF  ELECTRICITY. 

parallel  to  the  needle  above.  The  lines  of  force  from  the  north  end 
of  the  needle  radiating  in  all  directions,  some  of  them  penetrate 
the  disc.  The  strip  A  B  is  therefore  a  conductor  moving  across  a 
magnetic  field  and  application  to  each  half  of  AB  of  the  right 
hand  rule  for  direction  of  induced  currents  (Par.  422)  shows  that 
a  current  flows  from  B  to  A,  returning  by  the  right  and  left  as 
shown  by  the  broken  lines.  But,  such  a  current  will,  in  accord- 
ance with  Oerstedt's  rule  (Par.  345),  cause  the  north  pole  of  the 
needle  to  move  off  in  a  clockwise  direction. 

Such  induced  currents  flowing  around  through  the  mass  of  the 
conductor  and  returning  upon  themselves,  are,  from  analogy  with 
the  circular  whirls  produced  in  running  streams,  called  eddy 
currents. 

Reflection  will  show  that  if  the  copper  plate  in  the  above  experi- 
ment be  suspended  by  a  thread  and  the  needle  be  rotated  just 
below  it,  the  plate  will  take  up  a  motion  of  rotation  in  the  same 
direction.  On  account  of  the  feebleness  of  the  needle,  it  is  custom- 
ary, in  showing  this  fact  experimentally,  to  employ  an  electro- 
magnet. The  principle  involved  in  these  experiments  is  applied 
in  the  induction  motor,  a  machine  to  be  described  later. 

429.  Foucault's  Experiments. — Foucault  arranged  a  copper  disc 
to  rotate  like  a  circular  saw  between  the  poles  of  an  electro-magnet. 
When  the  current  was  off,  the  only  energy  required  to  rotate  the 
disc  was  that  to  overcome  the  friction  of  its  bearings,  but  as  soon 
as  the  cores  were  magnetized,  resistance  to  the  turning  was  experi- 
enced. If,  in  spite  of  the  resistance,  the  disc  was  forced  to  rotate, 
it  rapidly  grew  hot.  Foucault  showed  that  this  heating  was  due 
to  the  circulation  of  the  eddy  currents  in  the  copper.  If  narrow 
radial  slits  were  sawed  in  the  disc,  thus  interrupting  the  paths  of 
these  circular  currents,  the  resistance  to  turning  and  the  accom- 
panying heating  effect  disappeared.  On  account  of  these  experi- 
ments, eddy  currents  are  often  spoken  of  as  Foucault's  currents, 
but  the  two  names  are  synonymous. 

In  order  to  produce  an  electric  current  there  must  be  an  expendi- 
ture of  energy.  This  heating  effect  therefore  represents  waste 
energy  and  is  of  much  importance  in  any  electrical  apparatus  in 
which  the  flux  is  frequently  varied,  such  as  electro-magnets, 
transformers  and  electric  generators  and  motors,  especially  those 
employing  alternating  currents.  To  avoid  this  loss  of  energy, 
and  also  to  avoid  excessive  heating,  the  cores  of  electro-magnets 


ELECTRO-MAGNETICS.  333 

are  sometimes  made  of  bundles  of  soft-iron  wires,  and  the  cores  of 
transformers  and  of  the  field  magnets  and  armatures  of  electric 
machines  are  laminated,  or  built  up  of  many  thin  sheets  of  soft 
iron,  the  principle  being  that  since  the  eddy  currents  flow  in  closed 
curves  whose  planes  are  perpendicular  to  the  lines  of  force  of  the 
core,  they  may  be  checked  if  the  cores  be  split  up  by  planes  parallel 
to  the  lines  of  force. 

430.  Lenz's  Law. — If  a  copper  cylinder  be  suspended  by  a  thread 
so  as  to  hang  between  the  poles  of  an  electro-magnet,  and  if  this 
thread  be  twisted  and  then  released,  the  cylinder  by  its  weight 
will  cause  the  thread  to  untwist  and,  if  the  current  be  turned 
off,  will  rotate  rapidly.  If  now  the  current  be  turned  on,  the 
rotation  will  be  instantly  checked  as  if  an  invisible  brake  had 
been  applied. 

The  principle  involved  in  this  phenomenon  was  given  by  Lenz 
in  the  form  of  a  general  law  to  the  effect  that  the  currents  induced 
by  moving  a  conductor  in  a  magnetic  field  are  of  such  direction  that 
their  reaction  tends  to  stop  the  movement  which  produces  them. 

The  following  illustration  will  make  this  clear.  Fig.  202  repre- 
sents the  same  arrangement  of  two  rails  and  a  sliding  wire  as  ex- 


plained in  Par.  425.  If  A B  be  pushed  in  the  direction  F,  a  current 
will  be  induced  flowing  from  A  to  B  (Par.  422).  AB  is  therefore 
a  conductor  carrying  a  current  and  placed  in  a  magnetic  field. 
By  Par.  352  it  is  acted  upon  by  a  force  in  the  direction  R,  that  is, 
diametrically  opposed  to  F. 

The  foregoing  affords  the  correct  explanation  for  the  electrical 
damping  referred  to  in  Par.  379. 

431.  Transformers.— It  was  shown  in  Par.  425  that  the  E.  M.  F. 
induced  in  a  coil  varies  with  the  number  of  lines  of  force  introduced 
or  withdrawn  in  a  given  time.  The  flux  produced  within  a  coil 
varies  with  the  permeability  of  the  core.  If  a  coil  be  wrapped 


334 


ELEMENTS  OF  ELECTRICITY. 


upon  a  soft  iron  core,  a  current  flowing  through  this  coil  will  pro- 
duce many  more  lines  of  force  within  the  coil  than  would  be 
produced  if  the  inner  core  were  absent.  The  inductive  effect  is, 
therefore,  very  greatly  increased  by  inserting  in  the  coil  an  iron 


core. 


Fig.  203. 


Fig.  203  represents  an  iron  rod  upon  which  is  wrapped  the 
primary  coil  and  on  top  of  this  the  secondary.  It  will  be  seen  that 
any  lines  of  force  produced  in  the  primary  must  of  necessity  be 
embraced  by  the  secondary.  The  following  consideration  will 
show  that  this  arrangement  may  be  still  further  improved.  The 
lines  of  force  which  emerge  from  one  end  of  the  iron  core  must 
pass  through  the  air  to  enter  the  other  end.  This  long  air-gap  in 
the  magnetic  circuit  very  materially  reduces  the  total  flux  (Par. 
401).  It  is  therefore  better  to  bend  the  iron  rod  into  a  ring,  or 
similar  closed  figure,  so  that  the  entire  paths  of  the  lines  of  force 
will  lie  in  iron. 


Fig.  204. 

Faraday  devised  the  arrangement  shown  in  Fig.  204,  a  soft  iron 
ring  A,  on  one  side  of  which  is  wrapped  the  primary  P,  and  on 
the  other  side  the  secondary  S.  When  a  current  /  is  sent  through 
P  as  indicated,  clockwise  lines  of  force  are  produced  in  the  iron 
core  A.  When  these  lines  penetrate  S,  a  current  /'  is  induced,  its 


ELECTRO-MAGNETICS.  335 

direction  being  as  shown.  If  the  current  /  produces  N  lines  of 
force  and  if  there  are  n  turns  in  P,  the  work  done  in  P  is  InN 
ergs  (Par.  358).  If  there  are  n'  turns  in  S,  the  work  done  as  these 
N  lines  penetrate  S  is  I'n' N  ergs.  The  work  in  the  two  coils 
being  equal, 

InN^J'n'N 

and  since  in  each  coil  this  work  is  done  in  the  time  t,  we  may  write 

N      T,  ,N 

In—  =  I'n'  -— 

t  t 

But  (Par.  425)  n  N/t  is  the  E.  M.  F.  in  the  primary  and  n'  N/t 
is  that  in  the  secondary.  Representing  these  by  E  and  Er  respec- 
tively 

IE  =  I'Ef 

or  I:I'=E':E 

that  is,  the  currents  are  to  each  other  inversely  as  the  number  of 
turns  in  the  respective  coils;  the  voltages  are  to  each  other  directly 
as  the  number  of  these  turns.  In  the  secondary  coil,  the  current 
and  voltage  vary  reciprocally,  that  is,  as  one  increases,  the  other 
decreases  so  that  their  product  is  constant.  Should  there  be  ten 
times  more  turns  in  the  secondary  than  in  the  primary,  the  in- 
duced current  in  the  secondary  will  be  only  one-tenth  of  that  in 
the  primary,  but  its  voltage  will  be  ten  times  greater. 

Since  either  coil  may  be  used  as  the  primary,  the  other  one  being 
the  secondary,  it  is  possible  with  this  arrangement  to  trans- 
form at  will  a  changing  current  (i.  e.,  one  which  is  increasing  or 
decreasing)  into  another  whose  voltage  is  either  higher  or  lower 
than  that  of  the  original  current.  For  this  reason  it  is  called 
a  transformer,  this  particular  one  being  known  as  Faraday's 
ring  transformer.  Those  which  increase  the  voltage  are  called 
step  up  transformers;  those  which  lower  it  are  called  step  down 
transformers. 

The  assumption  above  that  the  work  in  the  secondary  is  equal 
to  that  in  the  primary  is  not  strictly  correct.  There  is  always 
some  magnetic  leakage  and  some  of  the  lines  produced  in  the 
primary  do  not  penetrate  the  secondary.  Again,  a  part  of  the 
energy  of  the  primary  is  wasted  in  producing  eddy  currents  in 
the  core  and  another  portion  in  overcoming  hysteresis  (Par.  399). 
This  waste,  however,  is  reduced  to  a  minimum  by  constructing 


336 


ELEMENTS  OF  ELECTRICITY. 


the  core  of  thin  punchings  of  soft  iron  of  the  shape  shown  in  Fig. 
205.  This  lamination  of  the  core  avoids  eddy  current  losses  (Par. 
429) ;  and  the  two  coils  being  wrapped  one  above  the  other  around 
the  central  portion  and  the  magnetic  circuit  being  complete  to 
the  right  and  left,  the  leakage  is  very  small.  In  the  best  modern 
transformers,  the  total  loss  is  less  than  three  per  cent. 


Fig.  205. 

Since  induction  is  an  effect  of  changing  currents  only,  trans- 
formers have  no  application  to  steady  currents  but  find  their 
most  useful  employment  in  connection  with  alternating  currents. 
They  will  therefore  be  discussed  further  when  that  subject  is 
reached. 

432.  Self-induction. — The  induction  considered  in  the  preced- 
ing pages  and  revealed  by  E.  M.  F.  induced  in  one  circuit  by  vary- 
ing the  field  of  another  and  neighboring  current,  is  called  mutual 
induction.  Induction  is,  however,  still  more  general  and  inductive 

effects  are  pro- 
duced in  a  circuit 
by  varying  the 
field  produced  by 
the  current  flowing 
in  the  circuit  itself. 
This  phenomenon 
is  called  self-indue- 
206-  turn. 

For  example,  if  a  current  I  be  sent  around  the  circular  coil  AB 
(Fig.  206),  a  field  will  be  produced  within  this  coil  in  the  direction 


ELECTRO-MAGNETICS.  337 

H.  But,  we  have  seen  (Par.  421)  that  if  lines  of  force  be  thrust 
into  this  coil  in  the  direction  H,  there  will  be  induced  an  E.  M.  F. 
in  the  direction  EB,  that  is,  opposed  or  counter  to  the  original 
E.  M.  F.  Therefore,  the  effect  of  self-induction  is  to  oppose  any 
increase  in  the  current,  and  this  explains  why  when  a  circuit  is 
closed  the  current  is  retarded  and  does  not  instantly  rise  to  its 
full  value.  It  is  also  seen  that  if  a  current  flowing  in  this  circuit  be 
decreased,  the  self-induction  of  the  circuit  delays  this  decrease 
and  causes  the  current  to  linger,  so  that,  in  general,  we  may  say 
that  self-induction  tends  to  prevent  any  change  in  the  field  em- 
braced by  a  circuit  and,  consequently,  in  the  current  flowing  in 
the  circuit. 

If  a  piece  of  soft  iron  be  inserted  in  the  coil  AB,  the  strength  of 
the  field  H  is  greatly  increased  (Par.  390) .  Hence,  the  induction 
of  a  circuit  embracing  a  magnetic"  substance  is  very  much  greater 
than  the  induction  of  the  circuit  alone. 

433.  Measure  of  Self-induction. — Since  induction  is  common  to 
all  circuits  and  since,  especially  in  dealing  with  alternating  cur- 
rents, it  must  frequently  be  taken  into  account,  it  is  necessary 
that  we  should  have  some  definite  measure  of  this  property  and 
some  concrete  unit  by  which  we  may  give  concise  expression  to 
its  value. 

If  we  had  to  deal  with  circular  coils,  each  of  a  single  turn,  we 
could  use  the  term  "induction"  in  its  primitive  significance  of 
"crop  of  lines  of  force  produced"  (Par.  400),  and  could  measure 
induction  by  the  change  in  the  number  of  lines  embraced  by  the 
coil  when  the  current  was  increased  or  decreased  one  unit.  But 
this  simple  conception  is  complicated  by  the  fact  that  the  induc- 
tive effect  varies  with  the  geometric  form  of  the  circuit.  For 
example,  suppose  that  in  a  given  circular  coil  of  wire  an  increase 
of  one  unit  in  the  current  should  increase  by  two  the  number  of 
lines  embraced.  If  the  wire  be  now  coiled  into  two  smaller  circles, 
but  otherwise  not  changed,  an  increase  of  one  unit  in  the  current 
would  again  add  two  lines,  but  these  two  lines  would  penetrate 
each  turn  of  the  coil  and  the  counter  E.  M.  F.  produced  would 
be  twice  that  produced  in  the  original  circuit.  Finally,  if  the  wire 
be  folded  at  its  middle  point  and  then  made  into  a  coil  (Par.  315) 
the  unit  current  would  again  produce  the  two  lines  but  they  would 
be  in  opposite  directions  and  hence  (b,  Par.  418)  the  resultant 
field  would  be  zero  and  there  would  be  no  counter  E.  M.  F.  pro- 


338  ELEMENTS  OF  ELECTRICITY. 

duced.  It  is  agreed,  therefore,  to  use  the  term  "induction"  in  the 
sense  of  "cutting  of  lines  of  force."  Thus,  in  the  illustration  above, 
if  two  lines  be  cut  twice,  the  cutting  is  four,  and  in  the  last  case 
the  cutting  is  zero.  From  this  point  of  view,  therefore,  the 
absolute  unit  of  self-induction  is  the  induction  of  that  circuit  in 
which  a  change  of  one  absolute  unit  of  current  produces  a  cutting 
of  one  line  of  force.  This  unit  has  received  no  name.  The  prac- 
tical unit  of  self-induction,  however,  is  called  the  henry  and  is 
defined  as  the  induction  of  that  circuit  in  which  a  change  of  one 
ampere  in  the  current  produces  a  cutting  of  one  hundred  million  (108) 
lines  of  force.  The  henry  is  therefore  109  absolute  units  of  self- 
induction. 

In  the  above  definition,  the  question  of  time  is  not  involved, 
that  is,  it  is  immaterial  whether  the  change  takes  place  rapidly  or 
slowly. 

434.  Inductance. — The  total  cutting  of  lines  of  force  caused  by 
a  change  of  one  ampere  in  a  circuit  is  called  the  inductance  of  the 
circuit  and  is  represented  by  the  symbol  L.  It  follows  that  if  the 
current  change  /  amperes,  the  total  cutting  of  lines  of  force  will 
be  N  =  LI.  If  this  change  takes  place  in  t  seconds,  the  average 
rate  of  cutting  will  be  N/t  or  Ll/t,  which,  as  we  have  seen  (Par. 
425)  is  the  counter  or  back  E.  M.  F.  produced  in  the  circuit.  This 
may  be  expressed  thus 

EB=-LI/t 

the  negative  sign  indicat- 
ing that  the  induced  E.  M.  F.  is  opposed  to  the  impressed  E.  M.  F. 
In  order  that  EB  should  be  expressed  in  volts,  the  above  must  be 
put  in  the  form 

;      ~ .  EB=~L-iwxt       v    ' ';./ -';; 

If,  however,  as  is  usually  the  case,  L  be  expressed  in  henrys 
(cutting  of  108  lines),  this  reverts  to  the  form 

EB=-LI/t 

If  in  this  last  expression  I  be  one  ampere,  t  be  one  second  and 
EB  be  one  (negative)  volt,  L  becomes  unity,  whence  we  may  say 
that  a  circuit  has  an  inductance  of  one  henry  if,  when  the  current  is 
varied  at  the  rate  of  one  ampere  per  second,  an  opposing  E.  M.  F.  of 
one  volt  is  set  up  in  the  circuit. 


ELECTRO-MAGNETICS.  339 

If  the  current  does  not  vary  at  a  uniform  rate,  the  instantaneous 
value  of  the  counter  E.  M.  F.  is 

F          T    dl 
EB=-L.Tt 

This  is  true  for  simple  coils,  since  the  field  of  a  coil  varies 
directly  with  the  current,  but  it  is  not  strictly  true  of  coils  with 
magnetic  cores,  because  as  these  cores  approach  saturation  the 
field  ceases  to  vary  directly  with  the  current. 

435.  Expression  for  Inductance  of  a  Coil. — An  expression  for 
the  inductance  of  a  coil  may  be  deduced  as  follows:  If  a  change 
of  I  amperes  in  the  current  flowing  in  the  coil  varies  the  field  of 
the  coil  by  <j>  lines  of  force,  and  if  the  coil  consists  of  N  turns,  the 
total  cutting  is  <£  N.  If  this  takes  place  in  t  seconds,  then 

But  in  the  preceding  paragraph  we  saw  that 
EB=-LI/t  volts 

L  being  the  inductance  of 

the  circuit  in  henrys.     Equating  these  expressions  and  striking 
out  common  factors 


In  Par.  400  it  was  shown  that  the  flux  produced  by  a  current 
of  /  amperes  in  a  coil  of  N  turns,  I  centimeters  long  and  of  r 
centimeters  radius,  wrapped  upon  an  iron  core  of  permeability 
I*  is 

0  =  - 


W.I 

This  was  deduced  under  the  supposition  that  the  core  was 
ring-shaped,  but  it  may  without  great  error  be  applied  to  coils 
with  straight  cores.  Substituting  in  (I)  above  and  striking  out 
common  factors,  we  have 

L  = 


L  being  the  inductance  of  the  coil  in  henrys. 

Had  the  core  been  of  air  or  other  non-magnetic  substance, 
/i  in  the  above  expression  becomes  unity. 


340  ELEMENTS  OF  ELECTRICITY. 

436.  Helmholtz's  Equation.  —  If  an  E.  M.  F.  E  be  impressed 
upon  a  circuit  of  resistance  R,  the  current  produced  will,  by 
Ohm's  law,  be  E/R  amperes.  If,  however,  there  be  inductance 
in  the  circuit,  a  counter  E.  M.  F.  of  L  .  dl/dt  volts  will  be  produced 
(Par.  434).  This,  if  acting  alone  in  the  circuit,  would  produce  a 
current  of 

L    dl 
-R    Wamperes 

The  current  actually  produced  is  therefore 

E      L    dl 
I  =  R~R'Tt  amperes  (I) 

If  E  and  L  are  constant,  the  variables  in  this  expression  are 
/  and  t.  By  transposing  and  dividing,  (I)  may  be  put  in  the  form 


R'1 

Rf 
The  integral  of  the  first  member  is  -^.     The  integral  of  the 

(V         \ 
-5  -  I  j  +  a  constant,  whence 

7?  /  /  TT*  \ 

-£-  =  -  log  I  -g  -  /  j  +  a  constant  (III) 

To  find  the  value  of  the  constant,  place  t  =  0.  The  first  member 
becomes  zero,  and  I  disappears  from  the  second  member,  for  at 
the  instant  Z  =  0,  no  current  is  flowing.  The  constant  there- 

fore =  log  ^ 
K 

Substituting  in  (III)  and  changing  signs  throughout, 

-T  =>•*(!-  <)-><*£ 


=  log       E 


ELECTRO-MAGNETICS. 

E 


341 


Whence 


E 
R 


_ 


€  being  2.7183,  the 
base  of  the  natural  system  of  logarithms.    Solving  for  /, 


or 


(IV) 


From  this  equation,  first  deduced  by  Helmholtz,  we  may 
determine  the  instantaneous  value  /  of  a  current  in  a  circuit  of 
resistance  R  and  inductance  L  at  any  time  t  after  the  circuit  is 
closed.  If  the  inductance  of  the  circuit  be  very  small,  that  is, 
if  L  be  very  small  as  compared  to  R,  the  second  term  in  the 
parenthesis  in  (IV)  disappears  and  the  current  rises  almost 
instantly  to  its  maximum  value.  If,  however,  the  inductance  be 


20         ao 
SECONDS 


60 


Fig.  207. 

great,  as  in  the  case  of  the  coils  around  a  large  electro-magnet, 
the  rise  of  the  current  may  be  gradual.  This  is  shown  graphically 
in  Fig.  207  in  which  the  curves  represent  the  growth  of  the  current 
urged  by  an  E.  M.  F.  of  ten  volts  through  circuits  of  a  resistance 
of  one  ohm  and  inductances  of  one,  ten  and  twenty  henrys, 
respectively.  If  the  inductance  be  one-tenth  of  a  henry,  the 
current  at  the  end  of  one  second  will  have  reached  a  value  of 
9.9996  amperes,  while  with  an  inductance  of  20  henrys,  this 
value  is  not  reached  in  three  minutes. 


342  ELEMENTS  OF  ELECTRICITY. 

437.  Induced  E.  M.  F.  at  Make  and  at  Break.— The  E.  M.  F. 

induced  when  a  circuit  carrying  a  current  is  broken,  is,  on  account 
of  the  great  rapidity  with  which  the  lines  are  removed,  much 
greater  than  that  induced  when  the  circuit  is  closed,  or  made. 
Interesting  experiments  have  been  devised  to  show  this  but  the 
following  considerations  will  show  that  they  are  hardly  needed. 
First,  when  the  wires  attached  to  the  terminals  of  an  ordinary 
dry  cell  are  touched  together,  an  E.  M.  F.  is  induced  counter  to 
the  E.  M.  F.  of  the  cell.  Reflection  will  show  that  it  must  be  less 
than  the  E.  M.  F.  of  the  cell  (that  is,  less  than  about  1.4  volts), 
for  if  it  were  greater,  a  reverse  current  would  be  sent  through  the 
cell,  and  if  it  were  equal,  no  current  would  flow,  both  of  which 
.suppositions  are  absurd. 

(f  Second,  when  the  wires  are  separated,  the  E.  M.  F.  induced  is 
many  times  greater  than  that  of  the  cell,  for  it  throws  a  spark 
across  the  gap  which  the  E.  M.  F.  of  the  cell  itself  could  not 
do. 

438.  The  Induction  Coil. — In  gasoline  engines,  the  mixture  of 
vapor  and  air,  in  the  proper  proportions  to  produce  the  most 
powerful  explosion,  is  introduced  in  the  cylinder  and  must  be 
ignited  just  as  the  piston  is  at  the  proper  point  in  its  stroke.    The 
ignition  of  this  explosive  mixture  is  -generally  brought  about  by 
an  electric  spark.     We  have  seen  (Par.  93)  that  to  produce  a 
spark  across  a  gap  of  even  one-hundredth  of  an  inch  requires  at 
least  300  volts,  and  this  is  considerably  increased  by  the  pressure 
of  the  vapor  in  the  cylinder.    It  would  be  impracticable  to  trans- 
port in  an  automobile  a  battery  large  enough  to  supply  this 
voltage  direct,  but,  by.  utilizing  the  principle  of  the  transformer 
as  applied  in  an  induction  coil,  the  necessary  voltage  may  be 
obtained  from  two  or  three  cells. 

The  induction  coil,  shown  diagrammatically  in  Fig.  208,  con- 
sists of  a  cylindrical  core  A  (made  of  a  bundle  of  soft  iron  wire 
so  as  to  avoid  eddy  currents),  upon  which  is  wrapped  the  primary 
coil,  a  few  turns  of  heavy  wire,  and  on  top  of  this,  the  secondary 
coil,  usually  many  thousand  turns  of  fine  wire.  In  the  large 
induction  coil  of  the  Military  Academy,  the  primary  consists  of 
208  feet  of  one-sixth  inch  copper  wire  and  the  secondary  of  49.3 
miles  of  wire,  1/133  of  an  inch  in  diameter.  In  the  circuit  of  the 
primary  there  is  a  battery  B  of  two  or  three  cells,  a  key  K,  and 
an  interrupter  7,  similar  to  the  one  described  in  Par.  410.  The 


ELECTRO-MAGNETICS. 


343 


ends  of  the  secondary  terminate  in  the  adjustable  spark  gap  S. 
If  used  for  ignition  purposes,  the  spark  gap  is  located  in  a  spark 
plug  which  is  screwed  into  the  cylinder  of  the  engine. 

The  operation  of  the  coil  is  as  follows:  When  the  key  K  is 
closed,  a  current  flows  through  the  primary  circuit  and  establishes 
a  field  from  right  to  left  through  the  coil.  The  core  A  becomes 
magnetized  and  attracts  the  armature  of  the  interrupter  I,  thereby 
breaking  the  circuit.  The  effect  of  breaking  the  circuit  is  to  with- 
draw suddenly  the  flux  through  the  core  and  this  induces  in  the 


Fig.  208. 

secondary  a  direct  E.  M.  F.  which  (Par.  431)  is  as  much  greater 
than  the  E.  M.  F.  of  the  primary  as  the  number  of  turns  in  the 
secondary  is  greater  than  the  number  in  the  primary.  In  other 
words,  the  coil  acts  as  a  step  up  transformer.  The  voltage  in  the 
secondary  is  high  enough  to  cause  a  rush  of  sparks  across  the 
gap  S.  When  the  circuit  is  restored  at  the  interrupter,  the  current 
again  flows  through  the  primary  and  re-establishes  the  field  in 
the  coil,  but  the  induced  E.  M.  F.  at  make  is  much  less  than  that 
at  break  (Par.  437),  and  sparks  are  not  generally  produced. 

To  cause  the  production  of  sparks  when  the  piston  is  at  the 
proper  point  in  its  stroke,  the  key  K  is  closed  by  a  revolving  cam, 
a  part  of  the  engine. 

It  should  be  remarked  that  the  invention  of  the  induction  coil 
antedates  by  many  years  the  invention  of  internal  combustion 
engines,  and  that  these  coils  have  other  important  uses  besides 
that  of  ignition. 

439.  Use  of  Condenser. — The  action  of  an  induction  coil  is 
much  improved  by  shunting  across  the  break  of  the  interrupter 


344  ELEMENTS  OF  ELECTRICITY. 

a  condenser,  shown  diagrammatically  at  G  in  Fig.  208.  A  correct 
explanation  of  its  operation  involves  a  discussion  of  capacity,  as 
will  be  shown  when  the  subject  of  alternate  currents  is  reached. 
For  the  time  being,  however,  the  following  explanation  will 
suffice.  As  preliminary  thereto,  we  assume  that  (a)  the  charge 
which  may  be  given  to  a  condenser  varies  with  its  capacity  and 
with  the  difference  of  potential  between  its  terminals  (Par.  93), 
and  (b)  the  induced  E.  M.  F.  at  break  is  a  hundred  or  more  times 
greater  than  that  at  make  (Par.  437). 

At  make,  when  the  current  is  flowing  across  7,  the  amount  of 
charge  in  G  depends,  from  the  above,  upon  the  difference  of  poten- 
tial between  E  and  F.  This  is  the  IR  drop  from  E  through  I  to  F, 
and  is  very  small,  consequently,  the  charge  in  G  is  small.  At 
break,  the  self -induced  current  in  the  primary  continues  to  flow 
in  the  same  direction,  therefore,  the  field  in  the  coil  is  maintained 
for  a  brief  interval.  Moreover,  the  induced  E.  M.  F.  being  great, 
and  the  circuit  being  broken  at  /,  E  is  at  a  much  higher  potential 
than  F,  and  a  large  charge  flows  into  the  condenser.  At  the  next 
instant,  the  induced  E.  M.  F.  dies  out,  there  is  now  no  difference 
of  potential  to  maintain  the  charge  in  G  and  the  condenser  dis- 
charges backward  through  E,  K,  B,  to  F.  This  discharge  passes 
through  the  primary  with  great  energy  and  opposite  in  direction 
to  the  original  current.  It  therefore  not  only  pushes  out  the  flux 
which  ran  from  right  to  left  through  the  coil,  but  establishes  a 
flux  in  the  coil  in  the  opposite  direction,  the  cutting  of  lines  of 
force,  and  hence  the  inductive  effect,  being  much  greater  than 
that  produced  by  simply  breaking  the  circuit  in  the  primary.  At 
the  next  succeeding  make,  the  current  through  the  primary  must 
rise  slowly  for,  before  it  can  establish  a  field  in  the  core,  it  must 
push  out  the  negative  field  already  ttiere.  Therefore,  the  condenser 
suppresses  any  sparks  at  make  and  increases  the  intensity  of  the 
sparks  at  break. 

440.  The  Bell  Telephone.— A  very  important  application  of 
the  principle  of  induction  is  the  telephone.  The  original  form,  as 
invented  by  Graham  Bell  in  1876,  is  shown  in  section  in  Fig.  209. 
It  consists  of  a  cylindrical,  hard-rubber  case  expanded  at  one 
end  and  containing  a  long  bar-magnet  M.  Just  in  front  of  the 
pole  of  the  magnet,  but  not  in  contact  with  it,  is  a  diaphragm  D 
of  thin  sheet  iron,  similar  to  that  used  for  tintypes.  Around  the 
same  pole  of  the  magnet  is  wrapped  a  coil  C  whose  free  ends  are 


ELECTRO-MAGNETICS. 


345 


attached  to  the  terminals  T.  Wires  extend  from  these  terminals 
to  the  other  end  of  the  line  and  are  there  attached  to  a  second 
instrument,  a  duplicate  of  the  first. 

When  sound  waves  strike  upon  the  diaphragm,  they  set  it  in 
vibration  and  it  alternately  approaches  and  recedes  from  the 
magnet.  As  it  approaches  the  magnet,  the  air  gap  between  the 
two  is  reduced  and,  the  diaphragm  being  of  iron,  additional  lines 
of  force  extend  from  the  magnet  to  it.  As  it  recedes,  the  number 
of  lines  decreases.  Since  these  lines  pass  through  the  coil  C, 


Fig.  209. 

variations  in  their  number  set  up  induced  currents  in  the  coil, 
and  hence  in  the  circuit  of  which  it  forms  a  part.  As  these  currents 
flow  in  one  direction  through  the  coil  at  the  far  end  of  the  line, 
they  increase  the  strength  of  the  enclosed  magnet  and  the  dia- 
phragm is  drawn  in.  As  they  flow  in  the  opposite  direction,  they 
weaken  the  magnet  and  the  diaphragm  springs  back.  The 
vibrations  at  the  near  end  of  the  line  are  therefore  reproduced  at 
the  far  end,  and  this  causes  the  sounds  to  be  repeated.  It  is  thus 
seen  that  the  Bell  telephone  was  originally  intended  to  be  used 
both  as  a  transmitter  and  as  a  receiver.  As  a  transmitter,  it  was 
used  as  a  mouth-piece;  as  a  receiver,  it  was  held  to  the  ear.  In 
more  recent  receivers,  instead  of  a  simple  bar-magnet  as  described 
above,  a  slender  horseshoe  magnet  with  soft  iron  pole  pieces  is 
used,  but  the  principle  is  the  same. 

441.  The  Transmitter. — The  E.  M.  F.  induced  by  the  vibra- 
tion of  the  diaphragm  of  the  Bell  telephone  is  necessarily  very 
small.  The  current  which  it  can  drive  over  a  long  line  of  con- 
siderable resistance  is  therefore  very  feeble,  so  feeble  in  fact  as 
to  restrict  its  use  to  short  distances.  This  difficulty  was  fusst 
overcome  by  the  Blake  transmitter.  More  recent  transmitters 
embody  the  same  principle  but  are  improved  in  details. 


346 


ELEMENTS  OF  ELECTRICITY. 


typical  form  is  shown  diagrammatically  in  section  in  Fig.  210. 
It  consists  externally  of  a  metal  case  with  a  suitably  shaped  hard- 
rubber  mouth  piece.  Within,  there  is  a  diaphragm,  insulated 
from  the  case,  and  a  cylindrical  metal  box.  In  the  back  of  this 
box  there  is  a  carbon  disc  and  in  the  front  a  second,  the  space 
between  the  two  being  packed  with  carbon  granules.  The  front 
carbon  disc  is  bolted  to  the  diaphragm.  The  sides  of  the  box  are 
lined  with  insulating  material.  A  wire  connected  to  the  diaphragm 
runs  to  a  battery  of  several  cells,  whence  the  circuit  is  completed 
through  the  primary  of  a  small  induction  coil  (a  step  up  trans- 
former), thence  through  the  metal  frame  supporting  the  trans- 
mitter back  to  the  enclosed  metal  box,  through  the  back  carbon 


Fig.  210. 

disc,  through  the  carbon  granules  to  the  front  carbon  disc  and 
thence  to  the  diaphragm.  There  is  an  arrangement,  shown  in 
Fig.  211,  by  which  this  circuit  is  broken  when  the  telephone  is 
not  in  use.  When  the  telephone  is  in  operation,  a  current  flows 
through  the  circuit  but  the  resistance  of  the  carbon  granules  is 
large  and  the  actual  amount  of  the  current  is  small.  When  the 
diaphragm  is  set  in  vibration  by  the  sound  waves,  it  compresses 
the  granulated  carbon  which,  as  we  have  seen  (Par.  285),  reduces 
the  resistance  of  the  carbon  and  allows  a  greater  current  to  flow 
from  the  battery  through  the  primary.  The  current  through  the 
circuit  therefore  varies  with  the  sound  waves  and  the  voltage  in 
the  primary  is  stepped  up  by  the  transformer  so  that  the  resistance 
of  the  line,  the  secondary,  may  be  overcome.  The  transmitter 
is  seen  to  be  somewhat  analogous  to  the  relay  used  in  telegraphy 
(Par.  412). 


ELECTRO-MAGNETICS. 


347 


442.  Operation  of  Telephone. — From  the  foregoing,  each  tele- 
phone consists  of  a  receiver,  a  transmitter,  a  transformer  and  a 
battery.  It  must  include  some  device,  usually  a  bell,  by  which 
calls  may  be  received,  and  also  some  arrangement  by  which  other 
stations  may  be  called.  Finally,  when  the  telephone  is  not  in  use 
the  circuit  of  the  battery  must  be  broken,  otherwise  the  battery 
would  soon  run  down. 


Fig.  211. 

There  are  many  telephone  systems  in  use.  Fig.  211  represents 
a  common  form,  the  hinged  doors  of  the  boxes  being  shown  as 
swung  to  one  side.  Its  operation  is  as  follows: 

(a)  To  call  a  station.  With  the  receiver  on  the  hook  switch, 
as  represented,  the  crank  handle  A  of  the  magneto  is  turned. 
(The  magneto  is  a  small  generator  whose  operation  will  be  ex- 
plained in  Part  V.)  A  current  traverses  the  following  path: 
B-C-D-E-F-G-H-J-K-L.  At  the  second  station  Z),  the  circuit 
is  precisely  the  same  and  the  bell  rings  at  both  stations. 


348  ELEMENTS  OF  ELECTRICITY. 

(b)  To  receive  a  message.    The  receiver  is  removed  from  the 
hook  and  held  to  the  ear.    The  hook,  freed  from  the  weight  of  the 
receiver,  rises  and  breaks  the  circuit  at  G  but  closes  it  at  M,  N 
and  0.     The  current  coming  in  from   D  follows  the  route 
E-F-0-R-S-B-C. 

(c)  To  send  a  message.    The  hook  being  up,  the  transmitter- 
battery-primary  circuit  is  closed  at  NM.    Currents  through  this 
circuit  are  stepped  up  in  the  secondary  S  and  follow  the  route 
given  above. 


ELECTRO-MAGNETICS.  349 


CHAPTER  34. 

AMMETERS   AND   VOLTMETERS. 

443.  Electrical  Quantities    to    be    Measured. — The    modern 
development  of  the  science  of  electricity  has  been  accompanied 
and  greatly  aided  by  the  production  of  ever  improving  instru- 
ments of  precision  for  the  rapid  and  accurate  measurement  of 
certain  electrical  quantities.     The  principal  of  these  quantities 
are: 

1  Resistance, 

2  Strength  or  intensity  of  current, 

3  Electro-motive  force, 

4  Electrical  power. 

The  measurement  of  resistance  was  explained  in  Chapter  26 
and  in  the  present  chapter  we  are  concerned  with  the  measure- 
ment of  current  and  of  electro-motive  force. 

444.  Electrical   Effects   Used   in    Measurements. — Electricity 
not  being  matter,  and  hence  being  imponderable  and  without 
physical  dimensions,  must  be  measured  indirectly  by  its  effects. 
These  are  usually  classed  under  four  heads,  viz.: 

1.  Thermal. — A  current  flowing  through  a  conductor  heats  it. 

2.  Electro-magnetic. — A  current  flowing  through  a  conductor 
produces  about  it  a  magnetic  field,     (a)  If  flowing  near  a  poised 
magnetic  needle,  the  needle  will  be  deflected,  or,  (b)  if  flowing 
around  a  soft  iron  core  the  latter  will  be  magnetized. 

3.  Electro-chemical. — (a)  A  current  flowing  through  acidulated 
water  will  decompose  the  same,  releasing  its  component  gases 
hydrogen  and  oxygen,  or  (b)  flowing  through  a  solution  of  a 
metallic  salt  will  decompose  the  salt,  depositing  the  metal  upon 
the  cathode  or  plate  by  which  the  current  leaves. 

4.  Physiological. — A  current  flowing  through  a  living  or  recently 
living  body  will  produce  certain  effects  such  as  muscular  twitchings 
and  contractions,  and  in  a  living  being  cause  more  or  less  painful 
sensations. 


350 


ELEMENTS  OF  ELECTRICITY. 


Of  the  above,  the  first  three  may  be  and  are  used  in  electrical 
measurements. 

445.  Effect  Best  Adapted  for  Measurement.— The  effect  best 
adapted  for  measurement  may  be  arrived  at  by  a  consideration 
of  the  following  experiments  after  Professor  Ayrton.  In  Fig.  212 


Fig.  212. 

B  represents  a  battery  with  which  are  connected  in  series  the 
various  pieces  of  apparatus  1,  2,  3,  4,  and  5,  through  which  there- 
fore the  same  current  flows. 

1  is  a  thermometer  around  whose  bulb  the  conducting  wire  is 
wrapped   and  which  dips  into  some  oil,   a  non-conductor  of 
electricity. 

2  is  a  magnetic  needle  in  whose  vertical  plane  and  around 
whose  pivot  as  a  center  the  wire  is  bent  in  a  circle. 

3  is  a  soft  iron  core  around  which  the  wire  is  wrapped.    On  top 
of  this  core  is  a  piece  of  soft  iron  fastened  to  the  hook  of  a  spring 
balance. 

4  is  a  glass  jar  upon  which  is  screwed  an  air-tight  cover.  Through 
this  run  the  two  wires,  each  terminating  in  a  platinum  plate 


ELECTRO-MAGNETICS.  351 

dipping  into  the  acidulated  water  with  which  the  jar  is  partly 
filled,  and  also  a  glass  tube  extending  nearly  to  the  bottom  of  the 
jar,  its  upper  portion  expanded  and  graduated  as  shown. 

5  is  a  glass  jar  partly  filled  with  a  solution  of  copper  sul- 
phate into  which  dip  two  copper  plates  to  which  the  wires  are 
attached. 

If  now  the  key  be  closed  and  the  current  be  allowed  to  flow  for 
a  short  time,  t,  the  following  effects  will  be  noted : 

1.  The  thermometer  will  indicate  a  rise  in  temperature. 

2.  The  needle  will  be  deflected  through  a  certain  angle  and  will 
remain  constantly  at  that  angle  as  long  as  the  current  flows. 

3.  The  soft  iron  core  will  become  magnetized  and  will  attract 
the  iron  block  so  that  a  force  of  x  ounces  must  be  exerted  upon 
the  spring  balance  to  tear  the  block  free. 

4.  Gas  will  be  released  at  the  surface  of  the  two  platinum  plates 
in  4  and  its  pressure  will  force  a  certain  number  of  cubic  centi- 
meters of  the  liquid  up  into  the  graduated  tube. 

5.  The  cathode  copper  plate  in  5  will  be  found  to  have  increased 
in  weight  due  to  the  deposition  of  fresh  copper  upon  its  surface. 

446.  Second  Experiment. — If,  beginning  under  the  original 
conditions  of  the  preceding  experiment,  the  key  be  closed  an 
interval,  t',  say  twice  as  long  as  the  original  t,  the  following  will 
be  observed: 

1.  The  thermometer  will  indicate  a  temperature  in  general 
greater  than  that  produced  by  the  first  experiment  but  bearing 
no  definite  relation  to  the  same. 

2.  The  needle  will  be  deflected  through  the  same  angle  as  before. 

3.  The  same  pull  will  be  required  to  release  the  soft  iron  block 
from  the  electro-magnet. 

4.  Twice  the  volume  of  gas  will  be  released  in  4. 

5.  Twice  the  weight  of  copper  will  be  deposited  on  the  cathode 
in  5. 

Assuming  that  the  current  has  been  the  same  in  these  two 
experiments,  we  may  conclude— 

(a)  That  the  temperature  indicated  by  the  thermometer  in  1 
varies  in  some  indeterminate  manner  with  the  time  and  that 
consequently  the  heating  effect  is  not  suitable  for  measurement. 


352 


ELEMENTS  OF  ELECTRICITY. 


(b)  That  the  electro-chemical  effects  vary  directly  with  the 
time  and  hence  if  reduced  to  a  common  unit  of  time  will  give  a 
definite  measure. 

(c)  That  the  electro-magnetic  effects  are  independent  of  time 
and  give  a  direct  measure  without  reduction. 

447.  Third  Experiment.— A  third  experiment  will  throw  further 
light  upon  this  subject. 

In  Fig.  213  B  represents,  as  before,  a  battery. 


Fig.  213. 

1  and  1A  thermometers,  as  before,  but  1A  has  more  turns  of 
the  wire  around  its  bulb  than  has  1  and  they  may  be  in  different 
sized  jars  which  contain  different  amounts  of  oil  and  perhaps 
different  kinds  of  oil. 

2  and  2  A  magnetic  needles  with  circular  coils  in  their  vertical 
plane,  the  coil  around  2  being  of  less  diameter  and  of  a  greater 
number  of  turns  than  that  around  2A. 

3  and  3 A  electro-magnets  differing  in  size  and  in  the  number 
of  turns  of  the  wire. 

4,  4A  and  4B  gas  voltameters,  4  being  two  in  parallel,  4A  a 
large  one  with  plates  far  apart,  4B  a  small  one  with  plates  closer 
together. 


ELECTRO-MAGNETICS. 


353 


5,  5A  and  55  copper  voltameters  arranged  similarly  to  the  gas 
voltameters. 

The  key  now  being  closed  for  an  interval  t,  during  which  the 
same  current  flows  through  the  entire  system,  the  following  will 
be  observed: 

1.  The  two  thermometers  will  indicate  a  rise  of  temperature 
but  the  indications  will  not  be  the  same  and  will  bear  no  apparent 
relation  to  each  other. 

2.  The  magnetic  needles  will  be  deflected  and  will  remain 
constantly  deflected  as  long  as  the  current  flows  but  the  angles 


4A 


4B 


Fig.  213. 

will  differ  in  the  two  cases  and  will  bear  no  apparent  relation  to 
each  other,  except  that  the  deflection  is  greater  in  the  instrument 
with  the  greater  number  of  turns. 

3.  The  electro-magnets  will  require  pulls  of  x  and  y  ounces 
respectively  to  separate  the  iron  blocks  but  these  pulls  will  bear  no 
apparent  relation  to  each  other. 

4.  The  amount  of  gas  released  in  each  of  the  two  gas  voltameters 
in  series  and  the  sum  of  the  amounts  released  in  the  two  in  parallel 
will  be  exactly  equal. 

5.  The  amount  of  copper  deposited  in  each  of  the  two  copper 
voltameters  in  series  and  the  sum  of  the  amounts  deposited  in 
the  two  in  parallel  will  be  exactly  equal. 


354  ELEMENTS  OF  ELECTRICITY. 

We  conclude  from  the  above: 

(a)  That  the  heating  effect  is  unsuitable  for  measurement. 

(b)  That  the  electro-magnetic  effect,  while  constant  for  the 
same  current  for  any  one  instrument,  is  yet  a  function  of  the 
mechanical  arrangement  of  the  instrument  and  would  be  different 
for  every  different  instrument. 

(c)  That  the  electro-chemical  effect  is,  within  wide  limits,  inde- 
pendent of  the  size,  shape,  and  arrangement  of  the  instruments. 

448.  Electro-Chemical    Effect   Selected   as    Standard. — As   a 

logical  consequence  of  the  above,  the  electro-chemical  effect  has 
been  selected  as  a  standard  for  the  measurement  of  electrical 
currents  and  the  Act  of  Congress  of  July  12,  1894,  legalized  the 
resolution  of  the  International  Congress  of  Electricians  of  the 
preceding  year  and  defined  the  practical  unit  of  current,  the 
ampere,  as  that  unvarying  current  which  flowing  through  an 
aqueous  solution  of  nitrate  of  silver  deposits  silver  at  the  rate 
of  .001118  gram  per  second. 

449.  Why  Silver  Selected. — The  current  is  defined  in  terms  of 
silver  deposited,  partly  because  silver  is  one  of  the  precious  metals 
and  when  deposited  from  solution  can  be  dried  and  weighed  with- 
out appreciable  error  due  to  increase  of  weight  by  oxidation  or 
other  chemical  change,  but  mainly  because  it  combines  high 
atomic  weight  (107.9)  with  monovalency  while  the  next  most 
suitable  metal,  copper,  whose  atomic  weight  is  63.6,  is  bivalent, 
so  that  a  given  current  flowing  for  a  given  time  will  deposit  nearly 
three  and  a  half  times  as  great  a  weight  of  silver  as  of  copper. 
Silver  is  therefore  used  in  delicate  measurements  of  small  currents 
but  it  is  expensive  and  for  large  currents  copper  is  employed. 

450.  Reason  for  Weight  Selected.— It  may  naturally  be  asked 
why  this  particular  weight  of  silver  was  selected  instead  of  some 
even  number,  such  as  .001  gram  for  instance.    The  reply  to  this 
is  that  the  absolute  C.  G.  S.  unit  of  current  had  already  been 
defined,  the  definition  being  b£sed  upon  electro-magnetic  effects 
(Par.i355),  and  from  many  elaborate  and  accurate  experiments 
the  amount  of  silver  deposited  by  the  unit  current,  and  hence  the 
amount  deposited  by  an  ampere,  had  been  determined. 

451.  Unsuitableness  of  Electro-Chemical  Effect  for  Industrial 

Needs.— While,  as  shown  above,  the  electro-chemical  effect  is 
selected  as  a  standard,  in  its  practical  application  to  most  in- 


ELECTRO-MAGNETICS.  355 

dustrial  needs  it  has  certain  insuperable  objections.  The  principal 
of  these  are  (a)  time  consumed  in  a  determination  and  hence 
inability  to  take  instantaneous  observations  and  (b)  lack  of  sensi- 
tiveness and  hence  inability  to  measure  small  effects. 

(a)  For  example,  just  as  the  steam  engineer  must  without  inter- 
mediate calculations  be  able  to  read  his  steam  gauge  at  any 
moment,  so  the  electrician  should  be  able  to  read  at  any  instant 
his  voltage  and  current.    The  determination  of  a  current  by  a 
voltameter  observation  is  a  laborious  matter  of  hours,  while  what 
is  needed  is  an  instrument  which  can  be  read  just  like  a  steam 
gauge  instantly  and  with  a  minimum  expenditure  of  labor.    To 
make  another  comparison,  to  use  a  voltameter  is  as  if  a  person 
desiring  to  find  out  the  time  was  compelled  to  take  a  set  of  astro- 
nomical observations  and  by  tedious  calculations  arrive  at  his 
result.    Naturally  it  is  simpler,  and  in  most  cases  preferable,  to 
read  from  a  clock  even  though  it  should  be  several  minutes  fast 
or  slow. 

(b)  Again,  the  sensitiveness  of  a  voltameter  is  not  great  and 
can  hardly  be  increased.    Many  currents  with  which  electricians 
have  to  deal  are  so  small  that  they  would  have  to  flow  for  days 
before  they  would  produce  enough  chemical  effect  to  be  suscep- 
tible of  accurate  measurement  and  even  this  supposes  what  is 
very  doubtful,  that  is,  that  a  current  could  be  kept  constant  for 
that  length  of  time. 

452.  Electro- Magnetic  Effect  Best  for  Practical  Measurements. 

—As  we  saw  in  the  account  of  the  preliminary  experiments  in 
Pars.  445,  446,  and  447,  the  magnetic  needle  in  each  case 
instantly  took  up  a  certain  position  and  retained  it  as  long  as  the 
current  remained  constant.  This  then  is  the  basis  of  the  majority 
of  instruments  in  practical  use. 

453.  Why  not  Selected  as  Standard. — The  question  now  arises 
why  then  was  not  the  electro-magnetic  effect  selected  at  the 
outset  as  the  standard.    The  reply  is  that  it  is  well-nigh  impossible 
to  construct  two  galvanometers  which  shall  be  duplicates,  and  it 
would  be  even  more  difficult  to  construct  a  duplicate  following 
the  specifications  which  such  a  definition  would  have  involved. 
On  the  other  hand,  as  we  have  seen  above,  the  electro-chemical 
effect  is,  within  wide  limits,  independent  of  instrumental  size  and 
shape  and  accurate  measurements  can  be  made  with  such  appara- 


356  ELEMENTS  OF  ELECTRICITY. 

tus  as  is  found  in  any  laboratory.  An  instrument  maker  could 
therefore  accurately  calibrate  a  galvanometer  by  the  somewhat 
tedious  voltameter  method,  as  explained  in  the  next  paragraph, 
and  thereafter  use  this  calibrated  galvanometer  as  a  standard  for 
the  rapid  calibration  of  others. 

454.  Calibration    of    Galvanometer. — The    galvanometer    to 
measure  current  is  calibrated  by  connecting  it  in  series  with  a 
voltameter,  noting  the  point  at  which  the  needle  stands,  deter- 
mining the  current  by  means  of  the  voltameter  and  marking  the 
galvanometer  scale  to  correspond,  then  repeating  this,  varying 
the  current,  and  so  on. 

For  small  currents  it  is  not  possible  to  calibrate  the  galvanom- 
eter directly  by  this  method,  but  since  galvanometers  follow  the 
fixed  law  that  the  deflecting  force  is  directly  proportional  to  the 
number  of  turns  in  the  coil,  it  may  be  calibrated  as  follows.  It 
is  first  calibrated  for  large  currents  as  explained  above,  with  say 
only  one  turn  in  the  coil.  The  soil  is  then  re- wrapped  with  finer 
wire  and  say  100  turns  are  put  on.  A  small  current  is  now  sent 
through  the  coil  and  produces  a  deflection  which  corresponds  to  i 
amperes  in  the  original  calibration.  We  know  that  the  effect  of 
the  actual  current  has  been  multiplied  100  times  by  the  number 
of  turns,  consequently  the  current  is  actually  only  2/100  amperes 
and  the  scale  can  be  so  marked,  and  so  on. 

The  sensitiveness  of  a  galvanometer  can  be  increased  to  a  very 
high  degree.  Ayrton  states  that  it  is  possible  to  measure  accurate- 
ly with  one  a  current  so  small  that  it  would  have  to  flow  for  a 
million  years  through  a  voltameter  before  it  produced  as  much 
chemical  action  as  a  current  of  one  ampere  could  produce  in  one 
hour. 

455.  Difference    between    Ammeters    and    Voltmeters. — The 

galvanometers  used  to  measure  current  are  called  Ammeters; 
those  to  measure  voltage  are  called  Voltmeters.  The  moving  parts 
of  an  ammeter  and  of  a  voltmeter,  of  the  kind  shortly  to  be 
described,  are  indistinguishable.  They  both  move  under  the  effect 
of  the  current  which  flows  through  them.  Ohm's  law  can  be 
written  E  =  RI.  As  applied  to  a  voltmeter  or  to  an  ammeter,  R 
is  the  instrumental  resistance  and  is  constant,  whence  it  is  seen 
that  the  voltage  is  always  some  constant  times  the  current  through 
the  instrument  and  it  might  be  thought  that  one  and  the  same 


ELECTRO-MAGNETICS.  357 

instrument  could  be- used  either  as  a  voltmeter  or  as  an  ammeter. 
If  its  scale  were  graduated  in  amperes,  the  readings  need  only  be 
multiplied  by  the  constant  R  to  convert  them  to  volts,  or  there 
might  perhaps  be  two  parallel  scales  under  the  same  needle,  one 
reading  amperes  and  the  other  volts.  If,  as  will  be  shown  later 
(see  Par.  474),  an  additional  piece  of  apparatus  be  employed,  the 
foregoing  conclusion  is  correct,  but  alone,  ammeters  and  volt- 
meters are  not  interchangeable.  The  following  explanation  of 
their  use  will  make  it  clear  why  they  are  not. 

456.  Essential  of  Measuring  Instruments. — The  first  require- 
ment of  every  measuring  instrument  is  that  when  used  it  should 
not  alter  the  quantity  which  it  is  to  measure.     Consequently, 
neither  the  ammeter  nor  the  voltmeter  when  properly  connected 
should  change  the  resistance  in  the  original  circuit.    Should  this 
resistance  be  changed,  the  current  will  change  in  accordance  with 
Ohm's  law  and  this  will  also  involve  change  in  voltage.     It  is 
interesting  to  see  how  these  two  instruments  fulfill  this  require- 
ment by  apparently  diametrically  opposite  methods. 

457.  Ammeters. — An  ammeter  measures  the  current  flowing 
in  the  circuit  at  the  point  at  which  it  is  connected.    It  is  inserted 
in  series  in  this  circuit  and  should  it  have  any  appreciable  resist- 
ance it  would  reduce  the  current,  that  is,  change  the  quantity 
it  is  to  measure.    The  resistance  of  an  ammeter  must  therefore 
be  so  small  that  its  effect  on  the  current  is  negligible. 

B 


VOLTMETER  ) 

<""">  /  AMMETER 

k oLJo *' 


DIMETER 

<^J 


Fig.  214. 

458.  Voltmeters. — A  voltmeter  measures  the  difference  of  po- 
tential between  the  two  points  to  which  it  is  connected.  These 
two  points  are  never  adjacent  but  in  general  are  far  apart  elec- 
trically. For  example,  they  may  be  the  terminals  of  a  battery 
(Fig.  214)  or  the  brushes  of  a  dynamo  or  the  leads  of  an  electric 
light  circuit.  Two  cases  may  arise:  (a)  there  may  be  a  broken 
circuit  between  the  two  points,  or  (b)  there  may  be  between  them 


358  ELEMENTS  OF  ELECTRICITY. 

a  closed  circuit  over  which  a  current  is  flowing.  In  either  case,  in 
order  that  the  original  status  of  the  circuit  as  regards  current 
should  be  changed  as  little  as  possible*  the  resistance  of  the  volt- 
meter must  be  great. 

(a)  If  the  circuit  between  the  two  points  be  broken,  the  resist- 
ance between  them  may  be  considered  as  infinite,  and  no  current 
flows.    When  the  voltmeter  is  inserted,  therefore,  its  resistance 
must  be  so  great  that  the  current  which  flows  through  it  is  so 
small  as  to  be  negligible. 

(b)  If  a  current  is  flowing  between  the  two  points,  in  order  that 
it  may  be  inserted  between  them  and  yet  not  disturb  the  original 
circuit,  the  voltmeter  must  be  connected  in  shunt.    The  voltmeter 
and  the  original  circuit  are  therefore  in  parallel  and  constitute  a 
divided  circuit  whose  resistance  is  less  than  that  of  the  original 
circuit  (Par.  293).     In  order  to  alter  the  original  resistance  as 
little  as  possible  the  resistance  of  the  voltmeter  must  be  as  great 
as  possible.    This  statement  hardly  requires  proof  but  may  be 
shown  mathematically  as  follows:  let  R  be  the  resistance  of  the 
original  circuit  between  the  two  points  and  x  be  the  resistance  of 
the  voltmeter.    The  joint  resistance  is  (Par.  293) 

Rx 

This  may  be  written 

7?2 

R- 


R+x 

whence  it  is  seen  that  the  joint  resistance  is  less  than  the  original 
resistance  by  the  fraction  „         and  approaches  the  original 

resistance  as  this  fraction  approaches  zero,  which  it  does  as  x 
increases. 

Practically,  the  resistance  should  not  be  made  excessive  for 
enough  current  must  be  let  through  the  voltmeter  to  actuate  the 
moving  parts.  The  average  resistance  of  a  voltmeter  reading  up 
to  100  volts  is  about  15,000  ohms. 

459.  Summary. — To  sum  up— 

(a)  The  moving  parts  of  an  ammeter  and  of  a  voltmeter  are 
the  same. 


ELECTRO-MAGNETICS.  359 

(b)  An  ammeter  is  always  connected  in  series  and  its  resistance 
should  be  as  near  zero  as  possible. 

(c)  A  voltmeter  between  two  points  in  a  circuit  carrying  a 
current  must  always  be  connected  in  shunt  and  its  resistance 
should  be  great,  so  great  that  the  current  through  it  is  neg- 
ligible. 

460.  Numerical  Example,  Voltmeter  Between  Two  Points  of 
a  Circuit.  —  The  following  numerical  example  will  bring  out  the 
effect  of  altering  the  resistance  of  a  voltmeter. 

Suppose  we  wish  to  measure  with  a  voltmeter  the  difference  of 
potential  between  AB,  the  terminals  of  the  battery  represented 
in  Fig.  214.  Suppose  the  E.  M.  F.  of  the  battery  to  be  10  volts, 
the  internal  resistance  to  be  1  ohm,  the  external  resistance  9  ohms. 

T^r  -j  rv 

The  current  is  ^—  -•  =  Q      1  =  1  ampere.     The  internal  drop  is 
KI  ~\~  T     y  ~i  -L 

Ir  =  1x1  =  1  volt,  hence  the  difference  of  potential  between 
A  and  B  is  9  volts.  To  measure  this  we  connect  up  as  shown. 
Suppose  the  resistance  of  the  voltmeter  to  be  9  ohms.  The  joint 
resistance  between  A  and  B  is  now  9/2  =4.5  ohms,  the  current 

amperes  and  the  difference  of  potential  between 


4  5  4-  1 

A  and  B  is  4.5x1.8  =  8.1  volts  or  0.9  less  than  it  was  before  the 
voltmeter  was  connected  up. 

Suppose  the  resistance  of  the  voltmeter  to  be  91  ohms.    The 

9X  91 
external  resistance  becomes  =  8.19  ohms  and  the  current 


1.08  -f  amperes.  The  difference  of  potential  between  A  and  B 
is  now  1.08x8.19=8.85  volts,  or  only  .15  volt  less  than  the 
original  voltage. 

Again,  increase  the  resistance  of  the  voltmeter  to  991  ohms. 
The  external  resistance  becomes  8.919,  the  current,  1.008  and 
the  difference  of  potential  between  A  and  B,  1.008  X  8.919  =  8.99 
volts,  or  only  .01  less  than  the  original  voltage. 

The  scales  of  voltmeters,  even  of  small  range,  are  hardly  ever 
graduated  closer  than  to  the  nearest  tenth  and  by  estimate  the 
position  of  the  needle  can  be  read  to  the  nearest  hundredth,  there- 
fore the  above  reading  is  within  the  limits  of  accuracy  of  the 
instrument.  A  further  increase  in  the  resistance  would  still 
further  increase  the  theoretical  accuracy.  The  resistance  of  the 


360 


ELEMENTS  OF  ELECTRICITY. 


usual  voltmeter  is  considerably  greater  than  the  991  ohms  assumed 
above. 

461.  E.  M.  F.  of  a  Cell  or  Battery.— Let  Fig.  215  represent  a 
cell  or  battery  whose  E.  M.  F.  is  E  and  whose  internal  resistance 


Fig.  215. 

is  r,  and  suppose  it  to  be  connected  up  with  a  voltmeter  whose 
resistance  is  R.    The  current  through  the  circuit  is  by  Ohm's  law 


-- 
~  R  +  r 

which  obviously  decreases 
as  R  increases.    The  above  may  be  written 

IR  +  Ir  =  E 
whence  IR  =  E  —  Ir 

But  IR,  the  external  drop,  is  what  the  voltmeter  reads  and  this 
is  always  less  by  the  quantity  Ir,  the  internal  drop,  than  E,  the 
total  E.  M.  F.  However,  this  internal  drop  decreases  as  /  gets 
smaller,  and  we  have  shown  above  that  /  gets  smaller  as  R,  the 
resistance  of  the  voltmeter  increases,  therefore,  the  greater  the 
resistance  of  the  voltmeter,  the  more  nearly  the  latter  will  read 
the  E.  M.  F.  of  the  cell  or  battery. 

462.  Classification  of  Ammeters  and  Voltmeters.  —  Ammeters 
and  voltmeters  may  be  classified  in  a  number  of  ways. 

1st,  according  to  the  kind  of  current  for  which  they  are  intended 
as  those  for 

(a)  Direct  Current, 

(b)  Alternating  Current. 

Some  alternating  current  instruments  may,  by  taking  certain 
precautions,  be  used  with  direct  currents  but  direct  current 
instruments  can  not  be  used  with  alternating  currents. 


ELECTRO-MAGNETICS.  361 

2d,  according  to  the  principle  upon  which  they  work,  as 

(a)  Hot  Wire  Instruments, 

(b)  Moving  Iron  Instruments, 

(c)  Moving  Coil  Instruments, 

(d)  Induction  Instruments. 

3d,  according  to  the  controlling  force,  as  those  with 

(a)  Gravity  Control, 

(b)  Spring  Control, 

(c)  Magnetic  Control. 

Bifilar  control,  control  by  torsion  and  control  by  the  earth's 
magnetism  can  not  be  used  in  these  instruments  and  gravity 
control  is  unsuitable  for  the  portable  class. 
4th,  according  to  the  manner  of  their  use,  as 

(a)  Portable, 

(b)  Switchboard. 

5th,  according  to  the  arrangement  of  their  scales,  as 

(a)  Dial  Instruments,  those  whose  pointer  moves  over  an  arc 

of  a  circle  like  the  face  of  a  clock. 

(b)  Edgewise  Instruments,  the  scale  being  on  the  surface  of  a 

cylinder  which  may  be  either  horizontal  or  vertical,  the 

pointer  moving  parallel  to  the  elements  of  the  cylinder. 

They  occupy  less  space  on  the  switchboard  than  the  dial 

instruments. 

Dial  scales  and  horizontal  edgewise  scales  usually  have  the  zero 
on  the  left,  but  for  some  purposes  it  is  of  advantage  to  have  the 
zero  at  the  center  although  this  shortens  the  available  scale  length 
by  one-half.  For  instance,  a  zero  center  ammeter  may  be  used  to 
measure  the  current  used  in  charging  a  storage  battery  and  also 
the  current  given  out  in  the  opposite  direction  by  the  battery 
on  discharge. 

The  number  of  kinds  is  so  great  that  the  mere  enumeration  of 
them  would  be  voluminous,  therefore  description  will  be  limited 
to  certain  typical  forms  in  general  use  in  this  country. 

463.  Hot  Wire  Instruments. — In  these  the  current  flows 
through  a  long  and  thin  platinum  wire  one  end  of  which  is  fastened 
rigidly,  the  other  directly  or  through  a  system  of  multiplying  levers 
to  a  movable  needle.  The  wire  is  drawn  taut  by  a  spring  fastened 
to  the  needle.  When  a  current  flows  through  the  wire  it  is  heated 


362  ELEMENTS  OF  ELECTRICITY. 

and  expands.  The  slack  is  taken  up  by  the  spring  and  this  causes 
the  needle  to  move  over  the  scale.  Since  the  heating  effect  varies 
as  the  square  of  the  current,  the  divisions  on  the  scales  of  these 
instruments  can  not  be  evenly  spaced.  They  may  be  used  with 
both  direct  and  alternating  currents.  They  are  not  largely  used. 

464.  Moving  Iron  Instruments. — These  are  also  called  "soft 
iron"  and  "gravity  control"  instruments,  and  are  largely  used 
abroad  and  to  a  less  extent  in  this  country.    They  may  be  used  for 
both  direct  and  alternating  currents.    There  are  many  kinds,  but 
the  following  will  illustrate  their ,  principle.    Fig.  216  represents 
an  end  view.    C  is  a  hollow  cylindrical  coil  around  which  the  cur- 
rent flows.    A  is  the  end  of  a  bar  of  soft  iron  attached  rigidly  to 
the  coil  or  to  its  frame,  its  length  parallel  to  the  axis  of  the  cylinder. 
B  is  a  second  bar  of  soft  iron  parallel  to  the  first  and  attached  to 
the  axis  Z),  which  is  free  to  rotate.    P  is  the  pointer  and  W  is  an 
adjustable  weight  of  non-magnetic  metal,  both  attached  to  the 

axis  D.  The  instrument  can  be  used 
in  but  one  position  and  when  the  weight 
W  is  properly  adjusted  the  pointer  P 
is  on  the  zero  of  the  scale.  Suppose  a 
current  to  flow  around  the  coil;  the 
bars  A  and  B  inside  of  the  solenoid  will 
both  be  magnetized  with  their  north 
poles  in  the  same  direction.  They  will 
therefore  repel  each  other,  B  will  move 
off  to  the  right,  the  pointer  will  sweep 
across  the  scale  and  the  weight  W  will 
be  lifted  and  oppose  an  increasing  torque  to  the  movement. 

In  a  second  class  of  these  instruments  the  moving  iron  piece  is 
drawn  into  a  solenoid  around  which  the  current  flows. 

Like  the  preceding,  the  scales  of  these  instruments  can  not  be 
evenly  spaced;  moreover,  they  are  liable  to  error  due  to  residual 
magnetism  in  the  soft  iron  bars  and  may  give  different  readings 
for  the  same  current  depending  upon  whether  the  current  has 
previously  been  increasing  or  decreasing.  These  disadvantages 
may  more  than  compensate  for  the  advantage  of  unvarying 
control. 

465.  Need  of  Ammeter  Shunts.— We  saw  in  Par.  457  that  an 
ammeter  is  inserted  in  series  in  the  circuit  and  should  oppose  no 


ELECTRO-MAGNETICS. 


363 


resistance  to  the  current.  Some  ammeters  must  measure  very 
large  currents,  so  large  that  the  conductor  must  have  a  cross- 
section  of  a  number  of  square  inches.  It  is  impracticable  to  con- 
struct an  instrument  whose  coils  should  even  approach  such  size, 
therefore  the  current  is  divided  at  the  instrument  and  some  very 
small  but  constant  fraction  is  sent  through  the  coil.  This  division 
is  made  by  means  of  a  shunt  (Par.  301).  For  small  portable 
instruments  the  shunt  is  within  the  case  and  such  are  said  to  be 
self-contained.  For  larger  switchboard  instruments  the  shunt  is 
generally  a  separate  piece  of  apparatus. 

466.  Switchboard  Shunts.— These  are  also  called  "station 
shunts."  They  consist  of  two  heavy  copper  terminals  A  and  B, 
Fig.  217,  which  are  connected  by  one  or  more  strips  or  sheets  C  of 


Fig.  217. 

a  special  alloy  of  very  small  temperature  coefficient.  The  strips  are 
used,  instead  of  one  piece  of  the  same  cross-section,  so  as  to  offer 
more  surface  for  cooling.  On  each  terminal  there  is  a  binding 
screw  D  and  E  to  which  the  leads  to  the  instrument,  flexible 
insulated  wire  cords  six  or  eight  feet  long,  are  attached.  Fig.  218 
shows  an  ammeter  and  its  shunt  in  position. 


Fig.  218. 

Suppose  the  resistance  of  a  station  shunt  for  an  ammeter  reading 
as  high  as  5000  amperes  to  be  .00001  ohm;  therefore,  with  full 
current  the  drop  from  D  to  E  is  .05  volt,  and  as  the  resistance  of 
the  instrument  and  its  leads  is  .5  ohm,  the  maximum  current 


364 


ELEMENTS  OF  ELECTRICITY. 


through  it  is  0.1  ampere.  The  resistance  of  the  leads  is  taken  into 
consideration  in  calibrating  the  instrument  and  they  should  on 
no  account  be  altered  by  lengthening  or  shortening.  They  and 
the  shunt  are  numbered  to  correspond  to  the  instrument  with 
which  they  are  to  be  used  and  can  not  be  used  with  any  other. 
These  leads  confer  a  two-fold  advantage;  1st,  they  permit  of  the 
position  of  the  ammeter  being  shifted  about  at  pleasure  and  with- 
out the  expense  caused  by  additional  lengths  of  heavy  copper 
mains  or  the  trouble  caused  by  the  mechanical  labor  in  bending 
and  arranging  these  mains;  2d,  the  ammeter  can  be  placed  at  such 
a  distance  from  the  mains  that  it  is  unaffected  by  the  field  pro- 
duced around  them  by  even  very  powerful  currents. 

467.  The  Weston  D.  C.  Ammeter.— The  Weston  instruments 
are  both  in  construction  and  accuracy  among  the  best.     In 


Fig.  219. 

principle  they  are  d'Arsonval  galvanometers  (Par.  378)  with 
certain  changes  by  which,  while  overcoming  the  structural  weak- 
ness of  the  d'Arsonval  instrument  and  making  it  fit  for  portable 
use,  the  requisite  sensitiveness  is  retained.  These  changes  are 
(a)  substituting  for  the  phosphor-bronze  suspension  filament 
suspension  of  the  coil  by  pivots  in  watch  jewels;  (b)  control  by 
coiled  hair  springs  instead  of  by  torsion  of  the  suspending  fila- 
ment; (c)  use  of  a  pointer  of  aluminum  instead  of  reflection  from 
a  mirror;  (d)  accurate  balancing  of  the  coil,  enabling  the  instru- 


ELECTRO-MAGNETICS. 


365 


merit  to  be  used  in  any  position;  (e)  improved  damping,  making 
the  instrument  absolutely  dead  beat  (Par.  379). 

They  are  of  many  types.  One  of  the  usual  forms  of  portable 
ammeter  is  represented  in  Fig.  219.  Its  case  is  of  pressed  brass 
or  copper  mounted  upon  a  wooden  base.  In  the  larger  switch- 
board instruments  the  case  is  of  cast  iron  which  has  the  advantage 
of  shielding  the  instrumental  field  from  perturbations  due  to 
external  fields. 

Within  the  case  and  nearly  filling  it  is  a  permanent  horseshoe 
magnet  M  (Fig.  220).  To  this  are  attached  the  soft  iron  pole 
pieces  N  and  S  which  include  between  them  a  cylindrical  opening. 
Were  these  pole  pieces  as  represented  in  a  in  the  following  figure 
the  greater  part  of  the  lines  of  force  would  cross  the  field  at  the 


Fig.  220. 


points  where  the  horns  of  N  and  S  approach  each  other  most 
closely.  The  field  would  therefore  be  crowded  at  these  points  and 
thin  at  the  intermediate  points.  However,  as  shown  in  b,  a  soft 
iron  cylinder  C  bolted  to  a  brass  cross  bar  B,  which  is  in  turn 
bolted  to  the  pole  pieces,  is  fastened  concentrically  in  the  space 
between  the  pole  pieces.  The  air  gap  between  the  cylinder  and 
the  pole  pieces  being  very  small  and  the  permeability  of  the 
cylinder  being  large,  the  lines  of  force  are  evenly  distributed  and 
the  field  is  very  uniform  (Par.  143).  Pivoted  in  watch  jewels  so 
as  to  turn  in  this  air  gap  is  the  rectangular  coil.  It  is  of  very  fine 
wire  wrapped  upon  a  light  aluminum  frame.  Upon  the  axis  of 
the  coil  are  mounted  from  top  to  bottom  the  upper  spiral  spring, 
the  aluminum  needle,  and  below  the  coil  the  lower  spiral  spring 
coiled  in  opposite  direction  to  the  first.  The  needle,  to  combine 
lightness  and  stiffness,  may  be  in  cross-section  either  tubular  or 
like  an  inverted  V.  The  end  which  travels  over  the  scale  is,  in 
portable  instruments,  compressed  sidewise  like  a  knife-blade  and 


366  ELEMENTS  OF  ELECTRICITY. 

in  switchboard  instruments  terminates  in  an  arrow-head.  The 
rear  end  of  the  needle  extends  beyond  the  axis  and  carries  an 
adjustable  counterweight.  There  are  also  similar  weights  at 
right  angles  to  the  needle  and  by  these  the  moving  parts  are  so 
balanced  that  the  instrument  may  be  used  in  any  position. 

The  binding  posts  by  which  the  current  enters  and  leaves  may 
be  placed,  as  shown  in  Fig.  219,  both  on  one  side,  or  may  be  both 
at  the  top  or  may  be  on  opposite  sides.  For  those  instruments 
whose  zero  is  at  one  end  of  the  scale  the  post  by  which  the  current 
must  enter  is  marked  conspicuously  +  as  shown  in  Figs.  219  and 
222. 

In  portable  instruments  with  self-contained  shunt,  the  latter 
is  a  strip  of  alloy  arranged  similarly  to  the  switchboard  shunt 
described  in  Par.  466  above.  The  fraction  of  the  current  which 
flows  through  the  coil  flows  first  to  the  upper  coiled  spring,  around 
this  spring  to  its  insulated  hub,  thence  to  the  coil,  around  the  coil 
and  out  by  the  lower  coiled  spring.  Fig.  221  illustrates  the  actu- 

^~ -^^  ating  forces.    The  lines  of  force  of  the 

field  run  from  N  to  S,  the  current  flows 
up  the  right  hand  side  of  the  coil  and 
down  the  left,  the  lines  of  force  of  the 
coil  run  as  shown  by  the  short  arrows. 
According  to  Maxwell's  law  the  coil 
will  therefore  turn  in  a  clockwise  direc- 
tion. Reflection  will  show  that  this 
could  not  be  used  with  an  alternating 
current. 

The  field  being  very  uniform  and  the 

resistance  to  torsion  which  the  coiled  spring  offers  increasing 
directly  with  the  angle  through  which  the  coil  turns,  the  scale  is 
regularly  spaced.  Parallel  to  the  scale  and  just  beneath  it  is 
fastened  an  arc  of  a  mirror.  By  covering  the  reflection  of  the 
needle  in  the  mirror  by  the  needle  itself,  the  observer  makes  sure 
that  the  eye  is  always  at  the  same  angle  with  reference  to  the 
needle  and  to  the  plane  of  the  scale  and  errors  due  to  parallax  are 
avoided. 

The  aluminum  coil  frame  rotating  in  the  strong  magnetic  field 
in  the  narrow  air  gap  makes  the  instrument  very  dead  beat.  The 
damping  effect  varies  as  the  square  of  the  magnetic  strength. 


ELECTRO-MAGNETICS. 


367 


468.  Weston    Portable    D.    C.    Voltmeter.— This    instrument 
closely  resembles  the  preceding.    The  one  represented  in  Fig.  222 


Fig.  222. 

differs  externally  in  having  above  the  +  binding  post  on  the  right 
a  push-button  switch  by  which  the  current  through  the  instrument 
may  be  closed  or  broken  at  will,  and  on  the  left  two  binding  posts 
by  either  of  which  the  current  may  leave.  The  object  of  these  is 
explained  below.  Internally  it  differs  in  having  no  shunt  but  a 
single  circuit  in  which  is  a  resistance  coil.  Suppose  connection 
to  be  made  with  upper  left  hand  binding  post  and  circuit  com- 


PUSH  BUTTON 


Fig.  223. 


pleted.  The  current  enters  on  the  right  (Fig.  223),  through  the 
button  switch,  thence  through  the  rotating  coil,  thence  through 
the  resistance  coil  A  and  out.  The  resistance  of  the  coil  A,  in 
the  particular  instrument  represented  in  the  figure,  is  so  adjusted 
that  a  difference  of  potential  between  the  terminals  of  the  instru- 
ment of  3  volts  will  drive  enough  current  through  to  carry  the 


368  ELEMENTS  OF  ELECTRICITY. 

needle  entirely  across  the  scale.  The  maximum  reading  is  there- 
fore 3  volts,  the  scale  is  graduated  and  numbered  on  the  lower 
side  accordingly,  and  the  corresponding  binding  post  is  plainly 
marked  3. 

If  connection  be  made  at  the  lower  left  hand  binding  post  the 
current  after  leaving  the  moving  coil  passes  through  the  resistance 
coil  B  and  out.  The  resistance  of  B  is  so  adjusted  that  the  instru- 
mental resistance  is  now  50  times  greater  than  before,  therefore 
a  voltage  50  times  greater,  or  150  volts,  would  be  required  to 
carry  the  needle  entirely  across  the  scale.  This  binding  post  is 
therefore  marked  150  and  the  upper  side  of  the  scale  is  numbered 
to  correspond. 

The  two  scales  are  usually  selected  so  that  the  larger  is  ten  or 
some  multiple  of  ten  times  the  smaller,  therefore  the  graduation 
of  the  two  scales  is  the  same  and  it  is  only  necessary  to  use  two 
sets  of  numbers. 

The  resistance  through  the  smaller  coil  of  a  15-150  voltmeter 
of  this  class  was  found  to  be  1772  ohms,  that  through  the  larger 
coil  17,720  ohms. 

These  instruments  are  calibrated  by  comparison,  usually 
through  a  potentiometer,  with  standard  cells.  The  importance 
of  accuracy  in  calibration  will  be  realized  when  the  statement  is 
made  that  in  electric  lighting  an  increase  of  3  per  cent  above 
the  normal  voltage  shortens  the  useful  life  of  a  lamp  one-half 
while  a  decrease  of  4  per  cent  below  normal  reduces  the  candle 
power  of  the  lamp  one-fifth. 


Fig.  224. 


469.  Multipliers.— The  foregoing  will  enable  us  to  understand 
an  auxiliary  piece  of  apparatus  used  with  voltmeters  and  called 
a  multiplier.  If  there  be  connected  in  series  with  a  voltmeter, 
as  shown  in  Fig.  224,  a  resistance  MP  which  is  so  adjusted  that 
the  resistance  between  C  and  M  is  ten  times  what  it  is  between 


ELECTRO-MAGNETICS. 


369 


C  and  D,  to  produce  a  given  deflection  of  the  needle  will  require 
a  difference  of  potential  between  C  and  M  ten  times  greater  than 
that  between  C  and  D.  Hence  to  get  the  correct  difference  of 
potential  between  C  and  M  the  readings  of  the  scale  must  be 
multiplied  by  ten.  Therefore,  a  multiplier  is  a  resistance  which, 
when  connected  in  series  with  a  voltmeter,  has  the  effect  of  multi- 
plying the  value  of  the  scale  divisions  by  a  certain  factor.  This 
factor  is  usually  marked  upon  the  case  of  the  multiplier. 

Multipliers  are  not  interchangeable  but  must  be  used  with  the 
particular  voltmeter  for  which  they  are  constructed.  The  second 
coil  B  in  Fig.  223  is  in  effect  a  self-contained  multiplier. 

470.  The  Weston  D.  C.  A.  C.  Voltmeter.— Consider  Fig.  221 
and  suppose  the  current  to  be  alternating.  The  direction  of  the 


Fig.  225. 

field  due  to  the  permanent  magnet  remains  constant  while  that 
through  the  coil  changes  with  change  of  direction  of  the  current. 
Hence  at  one  instant  the  needle  would  tend  to  turn  in  a  clockwise 
direction  and  at  the  next  instant  in  a  counter-clockwise  direction 
and  if  it  moved  at  all  would  only  quiver.  Therefore,  such  instru- 
ments cannot  be  used  with  alternating  currents. 

The  Weston  D.  C.  A.  C.  voltmeter,  to  overcome  this  objection, 
employs  the  principle  of  the  dynamometer  (Par.  382).  There  is 
no  permanent  magnet  but  within  the  case  and  perpendicular  to 
the  middle  of  the  scale  arc  there  is  a  thin  tubular  brass  frame 


370 


ELEMENTS  OF  ELECTRICITY. 


around  which  are  wrapped  many  turns  of  fine  wire.  This  cylinder 
is  separated  into  two  parts  by  a  narrow  gap  in  its  middle  (shown 
diagrammatically  and  much  exaggerated  in  Fig.  225)  and  in  this 
gap  there  turns  a  vertical  axis  which  carries  the  needle,  controlling 
spiral  springs,  movable  coil,  etc.,  as  in  the  instruments  already 
described.  The  movable  coil  C  is  circular  instead  of  rectangular 
and  normally  its  plane  makes  an  angle  of  45°  with  the  axis  of  the 
cylinder.  The  current  enters  at  E,  flows  around  the  coil  A,  thence 
to  the  upper  spiral  spring,  then  around  the  movable  coil  but 
opposite  to  its  direction  around  A,  thence  to  lower  spiral  spring, 
thence  around  coil  B  in  same  direction  as  around  A,  thence 
through  a  resistance  coil  and  out. 


A 

\ 
\       > 

>  \/ 

s 

Fig.  226. 

The  current  flowing  as  shown  by  the  arrows  in  Fig.  226,  the 
field  of  the  fixed  coils  will  be  in  the  direction  SN,  that  of  the 
movable  coil  will  be  in  the  direction  C  and,  in  accordance  with 
Maxwell's  law,  the  needle  will  move  in  a  clockwise  direction. 
When  the  current  reverses  its  direction  both  fields  are  also  reversed 
and  the  tendency  is  still'  for  the  needle  to  turn  in  a  clockwise 
direction,  hence  this  instrument  can  be  used  for  both  alternating 
and  direct  currents. 

When  the  movable,  coil  has  turned  until  it  is  at  right  angles  to 
the  outer  coils  the  deflecting  force  is  of  maximum  effect.  The 
graduations  of  the  center  of  the  scale  are  therefore  more  widely 
spaced  than  those  towards  the  extremities. 


ELECTRO-MAGNETICS. 


371 


The  movable  eoil  turning  in  a  weaker  field  than  in  the  D.  C. 
instruments,  the  damping  effect  is  much  less.  To  check  the 
oscillations  of  the  needle  and  bring  it  more  quickly  to  rest,  there 
is  near  the  bottom  of  the  coil  shaft  a  circular  plate  D  (Fig.  225) 
against  which  a  light  spring  brake  can  be  made  to  press. 

471.  The  Thomson  Inclined  Coil  Instruments. — These  are 
primarily  intended  for  alternating  currents  and  in  principle  do  not 
differ  greatly  from  the  one  just  described,  that  is  there  is  a  movable 
inner  coil  which  rotates  in  the  field  of  the  fixed  outer  coil. 


Fig.  227. 

Figure  227  represents  diagrammatically  one  of  these  instru- 
ments, a  voltmeter  with  edgewise  scale.  The  fixed  coil  A  makes 
an  angle  of  45°  with  the  horizontal  base  of  the  instrument.  Rotat- 
ing vertically  through  the  center  of  this  coil  is  the  shaft  which 
carries  the  two  non-magnetic  (phosphor  bronze)  spiral  control 
springs,  the  needle,  the  movable  coil  B  and  a  crescent-shaped 
aluminum  disc  D.  The  plane  of  the  rotating  coil  makes  an  angle 


372 


ELEMENTS  OF  ELECTRICITY. 


of  45°  with  the  base  of  the  instrument  and  is  also  placed  askew 
to  the  plane  of  the  fixed  coil.  The  current  enters  at  C,  flows 
around  A  in  the  direction  shown  by  the  arrow,  thence  to  the  upper 
spiral  spring,  thence  around  the  coil  B  in  the  direction  shown, 
thence  to  the  second  spiral  spring  and  out  through  a  resistance 
coil.  According  to  Maxwell's  law,  the  rotating  coil  tends  to  turn 
until  its  axis  is  parallel  to  that  of  the  fixed  coil  and  the  needle 
travels  across  the  scale  to  the  right. 


Fig.  228. 

The  inclined  coil  ammeters  differ  from  the  voltmeters  just 
described  in  having  no  rotating  coil  but  in  its  place  a  vane  or  flat 
sheet  of  soft  iron  V  (Fig.  228)  mounted  upon  the  axis  at  the  same 
angle  as  that  made  by  the  axis  of  the  rotating  coil  in  the  voltmeter. 
When  a  current  flows  through  the  fixed  coil,  the  vane  tends  to 
turn  to  the  position  V  parallel  to  the  lines  of  force  through  the 
fixed  coil  (Par.  143). 


Fig.  229. 


In  the  switchboard  instruments  of  this  type,  damping  is  effected 
by  the  aluminum  crescent  D  in  Fig.  227  turning  between  the  jaws 


ELECTRO-MAGNETICS. 


373 


of  two  jew's-harp  shaped  permanent  horseshoe  magnets  as  shown 
in  Fig.  229.  In  the  portable  instruments  a  friction  brake  or  air 
vane  is  used. 

472.  Use  of  Transformers  with  A.  C.  Instruments. — Alternating 
current  ammeters,  due  to  the  effects  of  self-induction  in  the  coils, 


AMMETER 

SLJO-N 
xxr 


Fig.  230. 

do  not  work  satisfactorily  with  shunts  and  if  the  current  to  be 
measured  is  of  such  size  that  in  a  D.  C.  instrument  a  shunt  would 
be  used,  the  current  through  the  ammeter  is  stepped  down  by 
means  of  a  series  transformer  as  shown  in  Fig.  230. 

On  the  other  hand,  if  the  pressure  in  an  alternating  current  circuit 
exceeds  about  1000  volts,  it  is  not  considered  safe  to  bring  this 


VOLTMETER 


Fig.  231. 

voltage  direct  to  a  voltmeter  and  it  is  stepped  down  by  a  potential 
transformer  as  shown  in  Fig.  231.  These  instruments  are,  of 
course,  graduated  to  read  the  current  or  the  voltage  in  the  primary- 
circuit. 


374  ELEMENTS  OF  ELECTRICITY. 

473.  Millivoltmeters. — If  there  be  constructed  an  instrument 
like  the  voltmeter  described  in  Par.  468  but  of  very  much  less 
internal  resistance  (10  instead  of  1700  ohms)  a  slight  difference 
of  potential   between  its  terminals  will  drive  enough  current 
through  the  coil  to  move  the  needle  over  an  extended  portion  of 
the  scale.    The  scale  can  therefore  be  graduated  to  show  much 
smaller  fractions  of  a  volt  than  is  possible  in  an  ordinary  volt- 
meter.   Such  an  instrument  reading  to  thousandths  of  a  volt  is 
called  a  millivoltmeter. 

474.  Millivoltmeters  as  Ammeters. — Suppose  a  millivoltmeter 
to  be  connected  to  the  extremities  of  a  shunt  AB  as  shown  in 
Fig.  232.    Suppose  it  has  a  scale  reading  to  300  millivolts  and  that 
its  resistance,  including  that  of  the  leads  which  accompany  it,  is 


Fig.  232. 

10  ohms.  A  difference  of  potential  between  AB  of  three- tenths 
of  a  volt  will  throw  the  needle  entirely  across  the  scale.  In  this 
case  the  current  through  the  instrument  is  from  Ohm's  law 

E       3 

-5  =  fpr  =  .03  ampere.    Suppose  a  current  of  300  amperes  to  be 

£1          1U 

flowing  in  the  main  circuit.  At  A  it  divides  inversely  proportional 
to  the  resistances  of  the  shunt  AB  and  of  the  instrument  and  its 
leads.  If  the  resistance  of  AB  be  made  ?k%v  ohm,  then  299.97 
amperes  will  flow  through  AB  and  .03  ampere  through  the 
instrument  and  the  needle  will  move  entirely  across  the  scale. 
The  divisions  on  the  scale  will  therefore  correspond  to  the  amperes 
in  the  main  circuit. 

If  the  resistance  of  A  B  be  made  ^VV  ohm,  then  30  amperes  in 
the  main  circuit  will  cause  the  needle  to  move  entirely  across  the 
scale  and  the  scale  divisions  will  each  correspond  to  one-tenth 
of  an  ampere. 


ELECTRO-MAGNETICS. 


375 


Finally,  if  the  resistance  of  AB  be  made  if  ohm,  the  scale 
divisions  will  correspond  to  one-hundredth  of  an  ampere  in  the 
main  circuit. 

It  is  therefore  possible,  by  employing  a  shunt,  to  use  a  milli- 
voltmeter  as  an  ammeter. 

475.  Millivoltmeter  Shunt. — Instead  of  separate  shunts  as 
described  above,  several  are  usually  assembled  in  one  case  as 
represented  in  Fig.  233.  The  current 
to  be  measured  is  always  brought  in 
at  the  upper  right  hand  post  and 
leaves  by  one  of  the  others  in  the 
upper  row.  The  millivoltmeter  is 
connected  with  the  corresponding 
posts  in  the  lower  row.  The  circuits 
are  as  shown  in  the  figure  which  repre- 
sents connections  made  to  read  a  cur- 
rent of  a  maximum  of  1.5  amperes. 
The  current  in  the  case  represented 
enters  at  A  and  leaves  at  B.  AC  is  a 
heavy  copper  bar.  D,  Dr,  D"  repre- 
sent diagrammatically  strips  of  resist- 
ance alloy.  The  numbers  on  the 
binding  posts  indicate  the  number  of 


Fig.  233. 


amperes  to  produce  a  total  scale  deflection  of  the  needle  when 
connection  is  made  at  the  corresponding  post.  These  shunts  and 
their  leads  must  be  used  with  the  particular  instrument  for  which 
they  are  constructed. 


376  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  35. 

HEATING   EFFECT   OF  ELECTRIC   CURRENT. 

476.  Work  Done  by  Electric  Current. — To  produce  an  electric 
current,  an  expenditure  of  energy  or  a  performance  of  work  is 
required.    According  to  the  fundamental  principle  of  mechanics, 
this  energy  is  not  lost  but  only  transmuted  and  must  be  given  back 
in  one  form  or  another  by  the  current.    In  a  cell,  for  instance,  there 
is  an  expenditure  of  chemical  energy  which  results  in  moving  Q 
units  of  electricity  through  a  difference  of  potential  V.    The  work 
done  is  therefore  W=QV  (Par.  72).    Since  there  is  no  current 
unless  there  be  a  complete  circuit,  each  of  these  Q  units  of  elec- 
tricity must  return  to  its  starting  point  and  in  doing  so  passes 
back  through  the  same  difference  of  potential  through  which  it 
was  moved,  or  gives  back  the  energy  expended  upon  it  in  the  first 
place.    A  current  flowing  in  a  circuit  must,  therefore,  perform 
work  of  some  kind,    (a)  In  Par.  215  we  saw  that  a  current  always 
heats  the  conductor  through  which  it  flows,     (b)   It  may,  in 
addition,  perform  electrolytic  (chemical)  work,  or  (c)  it  may, 
through  the  medium  of  machinery,  do  mechanical  work,  or  finally, 
(d)  it  may  do  magnetic  work.    Energy  is  also  expended  by  the 
current  in  establishing  a  magnetic  field  about  the  conductor,  but 
this  energy  need  not  be  considered  for  it  is  restored  when  the 
circuit  is  broken.    If  the  current  performs  neither  chemical,  nor 
mechanical,  nor  magnetic  work,  then  its  entire  energy  is  spent  in 
heating  the  circuit. 

We  shall  now  examine  into  this  heating  effect  of  the  current. 

477.  Determination  of  Laws  of  Heating  Effect. — An  experi- 
mental determination  of  the  laws  governing  the  heating  effect  of 
a  current  was  made  by  Joule  with  an  apparatus  similar  to  that 
shown  in  Fig.  234.    Through  the  cork  of  a  wide-mouthed  glass 
jar  containing  turpentine,  or  some  similar  non-conducting  liquid, 
were  run  two  heavy  wires  and  a  thermometer,  T,  all  of  which 
dipped  below  the  surface  of  the  liquid.    Between  the  ends  A  and  B 
of  the  large  wires,  there  was  connected  a  slender  bare  wire  of 


ELECTRO-MAGNETICS. 


377 


known  resistance,  preferably  of  manganin  (Par.  289).  The  jar 
was  then  connected  in  series  with  a  battery,  a  key  and  an  ammeter. 
Upon  closing  the  key,  the  current  flowed  through  the  circuit  and 
heated  the  small  wire,  which,  in  turn,  heated  the  turpentine.  The 
strength  of  the  current  was  read  from  the  ammeter.  The  increase 
in  temperature  of  the  turpentine  was  determined  by  the  thermom- 
eter, whence,  knowing  its  weight  and  its  specific  heat,  the  number 
of  heat  units  gained  could  be  determined.  The  length  of  time 
that  the  current  flowed  was  also  measured.  As  a  result  of  this 


Fig.  234. 

experiment,  Joule  found  that  the  amount  of  heat  produced  varied 
(a)  as  the  square  of  the  current,  (b)  as  the  resistance  of  the  con- 
ductor and  (c)  as  the  length  of  time  during  which  the  current 
flowed. 

478.  The  Joule.  —  Representing  by  H  the  quantity  of  heat 
produced,  Joule's  results  may  be  given  mathematical  expression 
as  follows: 


If  in  this  expression  /  be  one  ampere,  R  be  one  ohm,  and  t  be 
one  second,  we  have  H  =  1.  This  electric  unit  of  heat,  the  quantity 
of  heat  produced  by  a  current  of  one  ampere  flowing  for  one 
second  through  a  resistance  of  one  ohm,  has  been  named  the  joule. 
It  is,  however,  a  redundant  unit  since  we  already  have  in  the 
C.  G.  S.  system  the  small  calorie,  the  amount  of  heat  required  to 


378  ELEMENTS  OF  ELECTRICITY. 

raise  one  gram  of  water  through  one  degree  Centigrade  (Par.  11), 
The  joule  is  a  shade  less  than  one-quarter  of  a  calorie.  One  joule 
is  .24  of  a  calorie  and  hence  one  calorie  is  4.2  joules.  If,  therefore, 
H  represents  the  number  of  calories  produced,  Joule's  law  becomes 


479.  Theoretical  Deduction  of  Joule's  Law.  —  Joule's  law,  as 
given  in  the  preceding  paragraph,  may  also  be  deduced  from 
theoretical  considerations.  Thus,  suppose  a  current  of  strength  / 
is  flowing  through  a  simple  conductor  whose  resistance  is  R.  The 
difference  of  potential  between  the  ends  of  this  conductor  is  IR 
(Par.  298),  and  is  measured  by  the  work  done  in  moving  a  unit 
quantity  of  electricity  from  one  point  to  the  other  (Par.  72).  If 
the  current  flows  for  t  seconds,  the  total  quantity  conveyed 
between  the  two  points  is  Q  =  It,  therefore,  the  total  work  done 
is  IRxIt,  or  PRt,  this  energy  being  spent  solely  in  heating  the 
conductor.  To  reduce  this  to  ergs,  I  and  R  must  be  expressed  in 
absolute  units.  Since  one  ampere  =  10"1  absolute  units  of  current 
and  one  ohm  =  109  absolute  units  of  resistance  (Par.  427),  we  have 
the  total  energy  expended  =  /2^Xl07  ergs.  In  Par.  11  it  was 
shown  that  the  small  calorie  is  equivalent  to  4.2  XlO7  ergs.  To 
reduce  the  above  expression  to  calories,  we  must,  therefore, 
divide  it  by  this  number,  hence 

H  *JT2#*  XlO7)  -5-  (4.2  XlO7)  =  PRt/  '4.2  =  PRt  X0.24 
which  is  IstieVame  as  the  expression  in  the  preceding  paragraph. 


480.  Electric  Heating  of  Wires. — When  a  current  flows  through 
a  wire,  the  wire  is  heated.  The  heat  generated  in  the  wire  is  con- 
veyed away,  mainly  by  radiation  and  convection.  The  rate  at 
which  this  heat  is  dissipated  increases  as  the  temperature  of  the 
wire  exceeds  that  of  the  surrounding  medium.  The  temperature 
of  the  wire  continues  to  rise  until  the  loss  of  heat  by  radiation,  etc., 
exactly  balances  the  amount  generated  by  the  current.  Reflection 
will  show  that  since  the  heated  air  in  a  room  ascends,  a  wire  upon 
the  ceiling  will  radiate  its  heat  more  slowly  than  if  lower  down, 
also,  since  the  insulation  upon  a  wire  hinders  the  escape  of  the 
heat,  the  temperature  of  an  insulated  wire  carrying  a  current  will 
exceed  that  of  the  same  sized  bare  wire.  If  the  escape  of  heat  be 
still  further  impeded  by  enclosing  the  wire  in  a  wooden  moulding, 
as  is  sometimes  done,  its  temperature  may  reach  a  point  where 


ELECTRO-MAGNETICS,  379 

the  insulation  becomes  charred  or  even  where  the  woodwork  is 
set  on  fire.  For  this  reason,  most  insurance  companies  forbid 
the  use  of  these  wooden  ceiling  strips  and  specify  that  wiring 
must  either  be  exposed  or  enclosed  in  non-combustible  conduits, 
and  must  be  so  proportioned  that  its  temperature  shall  never 
exceed  a  certain  allowable  maximum. 

481.  Calculation  of  Temperature. — The  dissipation  of  heat 
by  a  wire  varies  with  the  material  of  which  the  wire  is  composed 
and  with  the  nature  of  its  surface,  with  the  extent  of  this  surface, 
with  the  excess  of  its  temperature  over  that  of  the  surrounding 
medium  and  with  the  nature  of  this  medium.  If,  when  its  tem- 
perature is  1°  C  above  that  of  the  surrounding  medium  it  emits  e 
calories  per  second  per  square  centimeter  of  surface,  it  will  emit 
Te  calories  per  square  centimeter  per  second  when  its  temperature 
is  T°  C  above.  If  its  length  be  I  centimeters  and  its  diameter  be  d 
centimeters,  its  surface  is  irdl  square  centimeters  and  its  emission 
per  second  is  Teirdl  calories.  During  this  time,  the  calories 
generated  per  second  by  the  current  are  I2.Rx0.24,  hence  when 
the  temperature  becomes  constant, 

Teirdl  =  72#X0.24 

Substituting  for  R  its  value  (Par.  285) 

I.P 


and  solving  for  7,  we  have 

o  /  T  /> 
I=( 


Applying  this  to  wires  of  the  same  material,  p  is  constant,  and 
if  the  wires  attain  the  same  temperature,  T  is  constant,  hence, 
the  current  to  raise  these  wires  to  the  same  temperature  varies 
as  the  square  root  of  the  cube  of  the  diameter  of  the  wires.  This 
formula  enables  us  to  calculate  the  size  of  the  fuse  wires  (Par.  306) 
which  will  melt  when  the  current  reaches  a  certain  maximum.  If 
the  fuse  wire  be  of  tin,  its  specific  resistance  p  is  13X10-6  ohms, 
and  e  is  about  .00025.  Its  melting  point  being  230°  C,  T  is  230 
minus  the  temperature  (Centigrade)  of  the  surrounding  air. 

482.  Localizing  the  Heating  Effect  of  a  Current.— If  a  current 
passes  through  two  portions  of  a  circuit,  each  of  the  same  resist- 
ance, the  amount  of  heat  developed  in  each  will  be  the  same.  If 


380  ELEMENTS  OF  ELECTRICITY. 

one  of  these  portions  be  a  large  wire,  several  hundred  yards  long, 
and  the  other  be  a  small  wire,  only  a  few  inches  in  length,  the  heat 
will  still  be  the  same  in  amount  but  in  the  case  of  the  large  wire 
it  will  be  distributed  over  its  entire  length  and,  on  account  of  the 
great  radiating  surface,  there  will  be  no  perceptible  rise  in  tem- 
perature. On  the  other  hand,  the  heat  is  concentrated  in  the 
small  wire,  which  can  not  dispose  of  it  by  radiation,  and  the  tem- 
perature of  the  small  wire  therefore  rises.  Such  is  the  principle 
upon  which  the  employment  of  electricity  for  heating  and  for 
lighting  is  based.  The  current  is  brought  to  the  required  spot 
through  wires  of  but  little  resistance  and  is  then  passed  through 
a  short  length  of  high  resistance,  the  development  of  heat  being 
thereby  localized.  If  the  portion  of  the  circuit  is  to  be  heated  to 
incandescence,  as  for  example  the  filament  in  an  incandescent 
lamp,  its  length  must  be  short  and  its  resistance  high.  If  it  is 
merely  to  be  warmed,  its  length  must  be  greater  and  its  resistance 
less.  The  following  examples  will  make  this  clear. 

483.  Electric  Fuzes.— Electric  fuzes  are  of  many  kinds.  Fig. 
235  represents  in  section  an  ordinary  blasting  fuze,  which  is  also 
variously  designated  as  a  primer,  a  cap,  or  a  detonator.  It  con- 
sists of  a  copper  case  A,  which  contains  the  explosive,  usually 


Fig.  235. 

mercuric  fulminate,  and  which  is  closed  by  a  plug  of  wood,  or  wax, 
or  sulphur  or  some  similar  cementing  material.  Through  this  plug 
pass  the  lead  wires  which  come  of  various  lengths  to  suit  the 
depth  of  the  drill  holes  in  which  the  blast  is  to  be  fired.  The  inner 
ends  of  the  lead  wires  are  connected  by  a  fine  platinum  "bridge"  B, 
about  .001  inch  in  diameter  and  one  quarter  of  an  inch  long. 
About  this  bridge  there  is  usually  wrapped  a  wisp  of  gun-cotton. 
The  passage  of  the  current  heats  the  platinum  bridge  and  ignites 
the  gun-cotton;  this,  in  turn,  ignites  the  fulminate  and  causes  the 
main  charge  to  explode.  These  fuzes  afford  the  simplest  and 
safest  method  of  firing  high  explosives,  and  the  only  certain 
method  of  blasting  under  water  and  of  causing  a  number  of  charges 
to  explode  simultaneously.  They  are  fired  from  a  safe  distance, 


ELECTRO-MAGNETICS.  381 

the  current  usually  being  supplied  from  a  hand  magneto,  although 
it  may  be  furnished  by  a  battery  or  taken  from  any  other  con- 
venient source.  In  the  military  service,  they  are  used  to  explode 
submarine  mines  and  to  fire  heavy  artillery.  For  this  latter  use 
they  are  charged  with  black  powder  instead  of  with  the  fulminate. 

484.  Electric  Welding. — If  two  metal  bars  connected  to  the 
terminals  of  a  generator  be  touched  together,  the  current  flowing 
through  the  resistance  along  the  surface  of  contact  will  cause  the 
local  production  of  great  heat.     Such  is  the  principle  of  the 
electric  welding  process  devised  by  Elihu  Thomson.    The  bars  to 
be  welded  are  brought  together,  the  necessary  current  is  turned 
on  and  in  a  very  short  time  the  metal  softens.    If  now  the  bars 
be  pressed  together,  a  weld  results.    In  this  manner  steel  axles 
two  inches  square  are  joined  in  a  little  over  a  minute  and  a  half. 

Alternating  current  is  used  almost  exclusively.  It  was  shown 
above  (Par.  477)  that  the  heating  effect  varies  as  the  square  of 
the  current.  By  a  simple  step  down  transformer  (Par.  431)  an 
alternating  current  may  be  transformed  into  another  whose 
voltage  is  low  but  whose  amperage  is  great.  Thus,  in  welding  the 
rails  of  trolley  lines,  the  current  is  taken  from  the  line  itself  but 
is  transformed  down,  currents  as  great  as  25,000  amperes  being 
employed,  and  the  rails  in  the  mean  time  being  squeezed  together 
with  a  pressure  of  thirty-five  tons. 

485.  The  Electric  Arc. — If  the  wires  attached  to  the  terminals 
of  a  battery  or  of  a  generator  be  touched  together,  completing  the 
circuit,  there  will  be  a  rush  of  current  which,  on  account  of  the 
localized  resistance,  will,  as  we  have  just  seen  (Par.  484),  develop 
great  heat  at  the  point  of  contact.    If  the  wires  be  now  separated 
about  an  eighth  of  an  inch  and  if  the  E.  M.  F.  between  them  be 
not  less  than  about  forty  volts,  the  current  will  continue  to  flow, 
being  conveyed  by  the  vapor  of  the  metal  volatilized  by  the  intense 
heat,  and  brilliant  light  will  be  emitted  by  the  glowing  ends  of 
the  wires  and  by  the  incandescent  vapor  between.     This  will 
continue  for  only  a  few  seconds  for  the  ends  of  the  wires  will 
rapidly  melt  off.     If  the  terminal  wires  be  attached  to  carbon 
rods  which  are  then  touched  together  and  separated,  the  same 
brilliant  light  will  be  produced  but  in  this  case  it  will  last  much 
longer  since  the  carbon  is  infusible.     The  flame,  or  rather  the 
stream  of  incandescent  vapor  between  the  carbons,  is  really  a 


382  ELEMENTS  OF  ELECTRICITY. 

flexible  conductor  composed  of  volatilized  carbon  and  has  the  prop- 
erties of  any  other  conductor  carrying  a  current.  For  instance, 
it  is  surrounded  by  a  magnetic  field  of  its  own  and  if  placed  in 
another  magnetic  field  will  tend  to  move  off  to  one  side  (Par.  356). 
Because  of  the  interaction  of  its  field  with  that  of  the  earth,  it  is 
generally  somewhat  curved,  and  on  this  account  it  was  named  the 
electric  arc.  If  the  field  be  strong  enough,  the  arc  may  be  pushed 
so  far  to  one  side  as  to  be  extinguished.  A  form  of  apparatus 
utilizing  this  principle  to  prevent  accidental  arcs  when  switches 
are  opened  is  called  a  "magnetic  blow-out." 

As  long  as  the  arc  is  maintained,  the  carbons  consume  away 
slowly  but  at  different  rates,  the  positive  carbon  wasting  much 
more  rapidly  than  the  negative.  The  tip  of  the  positive  carbon 
becomes  hollowed  out  into  a  little  pit,  called  the  crater;  on  the 
other  hand,  the  tip  of  the  negative  carbon  seems  to  receive  the 
particles  torn  away  from  the  positive  carbon  and  assumes  a  rather 
pointed  outline. 

The  chief  source  of  the  light  of  the  arc  is  the  crater  of  the 
positive  carbon,  the  arc  itself  emitting  but  little.  The  maximum 
temperature,  however,  exists  in  the  arc.  This  temperature,  the 
highest  yet  attained,  is  said  to  be  about  3500°  C,  or  twice  that 
required  to  fuse  platinum.  In  this  arc  the  most  infusible  sub- 
stances are  promptly  melted  and  even  vaporized. 

486.  The  Electric  Furnace. — Although  the  light  and  the  intense 
heat  produced  by  the  electric  arc  have  been  known  for  over  one 
hundred  years,  it  was  not  until  the  development  within  the  last 
thirty  years  of  machines  for  supplying  continuously  the  required 
current  that  the  use  of  the  arc  for  illuminating  purposes  became 
commercially  practicable,  and  its  utilization  on  a  large  scale  as  a 
source  of  heat  dates  from  the  still  more  recent  development  of 
such  great  sources  of  power  as  Niagara  Falls. 

Electric  furnaces  may  be  divided  into  two  general  classes  ac- 
cording as  the  body  to  be  heated  is  or  is  not  a  conductor.  If  it  be 
not  a  conductor,  it  must  either  be  placed  beneath  the  arc,  the 
heat  of  which  is  both  radiated  and  reflected  down  upon  it,  or  it 
must  be  intimately  mixed  with  powdered  carbon  or  other  conduct- 
ing substance,  the  passage  of  the  current  through  which  produces 
enough  heat  to  raise  the  temperature  of  the  body  to  the  required 
point.  If  it  be  a  conductor,  it  may  be  made  one  electrode  of  an 
immense  arc  and  be  heated  both  by  the  heat  radiated  from  the 


ELECTRO-MAGNETICS. 


383 


remaining  electrode  and  by  that  produced  by  the  passage  of  the 
current,  or  it  may  be  heated  by  the  passage  of  the  current  alone. 
Of  this  last  class  there  are  two  subdivisions  according  as  the  cur- 
rent is  conveyed  directly  through  the  body  or  is  produced  in  it 
by  induction. 

The  intense  heat  of  the  electric  furnace,  3500°  C  or  more,  has 
made  it  possible  to  fuse  silica  and  to  produce  therefrom  utensils 
of  great  use  in  the  laboratory;  has  permitted  the  reduction  of  the 
most  refractory  ores,  notably  those  of  aluminum;  has  enabled 
the  chemist  to  manufacture  graphite,  silicon,  etc.;  and  finally  has 
led  to  the  production  of  chemical  compounds  hitherto  unknown. 

487.  Moissan's  Furnace. — One  of  the  earliest  electric  furnaces 
was  that  devised  by  Moissan.  It  is  shown  in  section  in  Fig.  236 


Fig.  236. 


\ 


and  consists  of  a  chamber  scooped  in  a  block  of  lime  and  covered 
by  a  lid  made  from  a  second  block.  Lime  is  used  since  when  either 
hot  or  cold  it  does  not  conduct  appreciably.  The  carbons  enter 
through  grooves  on  opposite  sides.  The  body  to  be  heated  is 
placed  in  the  cavity  in  the  lower  block  and  the  heat  produced  by 
the  arc  is  reflected  down  upon  it,  that  is,  the  furnace  is  in  principle 
a  reverberatory  furnace. 

Furnaces  of  this  kind  can  not  be  made  on  a  large  scale.  They 
are  quite  small  and  are  used  for  fusing  small  amounts  of  refractory 
substances,  as  in  the  production  of  artificial  gems. 

488.  Manufacture  of  Carborundum. — In  1890  Acheson  made 
in  a  small  electric  furnace  a  crystalline  substance  which  he  sup- 
posed to  be  a  compound  of  carbon  and  corundum,  or  emery,  and 
he  accordingly  named  it  carborundum.  It  is  now  known  to  be 
the  carbide  of  silicon,  or  SiC.  It  is  of  great  hardness  and  has  come 
into  extensive  use  as  an  abrasive,  displacing  emery  in  the  various 
wheels,  grindstones,  whetstones,  polishing  cloths  and  powders. 


384 


ELEMENTS  OF  ELECTRICITY. 


It  is  made  on  a  large  scale  at  Niagara  Falls.  The  furnaces,  built 
of  brick  without  mortar,  are  some  fifteen  feet  long  by  seven  feet 
wide  and  high.  At  each  end  (Fig.  237)  there  are  built  into  the 
wall  heavy  copper  terminals  to  each  of  which  are  attached  the 
electrodes  proper,  sixty  carbon  rods,  three  inches  in  diameter  and 
two  feet  long.  These  electrodes  are  connected  by  a  core  of  crushed 
coke  about  nine  feet  long  and  two  feet  in  diameter.  Around  this 
core  there  is  packed  about  ten  tons  of  an  intimate  mixture  of 
34%  coke,  54%  sand,  10%  sawdust,  and  2%  salt.  The  salt  acts 
as  a  flux;  the  sawdust  keeps  the  mass  porous.  An  alternating 
current  of  4000  amperes  at  185  volts  is  turned  on.  This,  as  will 


Fig.  237. 

be  shown  in  the  next  chapter,  represents  about  1000  horsepower. 
In  a  short  while  a  large  amount  of  carbon  monoxide  is  produced 
and  burns  as  it  emerges  from  the  crevices  between  the  bricks.  In 
twelve  hours  the  furnace  becomes  red  hot  but  the  current  continues 
to  flow  for  twenty-four  hours  before  it  is  turned  off.  When  it  has 
cooled  sufficiently  the  furnace  is  dismantled.  The  interior  core 
of  coke  is  found  to  be  converted  into  graphite.  This  is  surrounded 
by  a  sixteen  inch  layer  of  iridescent  purplish  crystals  of  carbo- 
rundum. Outside  of  this  layer  there  are  slag-like  clinkers. 

In  a  somewhat  similar  manner  calcium  carbide,  CaC2,  is  made 
by  heating  a  mixture  of  lime  and  powdered  coke,  the  reaction 
being 

CaO+3C  =  CaC2+CO 

Calcium  carbide  is  used  for  the  production  of  acetylene  gas  for 
illuminating  purposes. 

489.  Manufacture  of  Aluminum. — Although  very  widely  dis- 
tributed, the  ores  of  aluminum  are  most  refractory  and  until 
recently  their  reduction  was  one  of  the  difficult  processes  in 
metallurgy.  The  metal  is  now  obtained  from  bauxite,  a  mineral 
containing  over  sixty  per  cent  of  aluminum  oxide,  A1203.  Alone, 


ELECTRO-MAGNETICS. 


385 


this  is  practically  infusible  but  dissolves  readily  in  fused  cryolite, 
a  double  fluoride  of  aluminum  and  sodium.  The  current  is  passed 
through  this  fused  mass,  aluminum  is  released  at  the  cathode  and 
oxygen  at  the  anode.  The  aluminum  being  liquid  settles  to  the 
bottom  and  is  drawn  off  from  time  to  time,  fresh  supplies  of 
bauxite  being  continually  added.  The  cryolite  is  not  affected. 
The  action  in  this  case  being  electrolytic  as  well  as  thermal, 
direct  current  must  be  used.  Aluminum  which  ten  years  ago  sold  for 
eight  dollars  a  pound  can  now  be  produced  with  profit  at  twenty- 
five  cents. 

490.  Electric  Iron  Furnaces. — There  is  an  increasing  use  of 
electric  furnaces  for  the  treatment  of  pig  iron  by  a  process  similar 
to  the  ordinary  open-hearth  process.  The  fused  metal  is  one  of 
the  electrodes,  the  other  consists  of  large  carbons  which  penetrate 
^the  dome  of  the  furnace.  The  arc  plays  between  these  carbons 
and  the  metal  beneath.  Suitable  linings  are  used  and  the  proper 
ingredients  are  added  to  the  molten  metal  to  remove  the  sulphur, 
phosphorus  and  other  objectionable  substances.  Such  furnaces 
are  now  made  of  a  capacity  of  fifteen  tons. 


Fig.  238. 

491.  The  Induction  Furnace. — The  induction  furnace,  recently 
introduced  for  the  manufacture  of  high-grade  steel,  is  a  special 
application  of  the  principle  of  the  transformer.  It  is  shown  dia- 
grammatically  in  Fig.  238.  P  is  the  primary  and  S  is  an  annular 
trough  of  non-conducting  fire-brick.  Into  this  trough  is  placed 
the  metal  which  is  to  be  treated  and  this  mass  of  steel  constitutes 


386  ELEMENTS  OF  ELECTRICITY. 

a  short-circuited  secondary  of  a  single  turn.  The  alternating  cur- 
rent in  P  is  stepped  down  in  S  to  a  current  of  large  amperage 
sufficient  to  bring  the  steel  to  a  molten  state.  At  the  proper  time 
the  required  amount  of  spiegeleisen  or  other  material  is  added. 
These  furnaces  have  been  made  large  enough  to  handle  ten  tons 
of  steel  at  a  charge. 


ELECTRO-MAGNETICS.  387 


CHAPTER  36. 

ELECTRIC   POWER. 

492.  Power  Defined. — If  a  certain  hoisting  engine  raises  a 
weight  from  the  ground  to  the  top  of  a  building  in  two  minutes, 
and  a  second  engine  raises  the  same  weight  the  same  height  in  one 
minute,  the  work  in  each  case  is  the  same  but  the  second  engine 
does  its  work  twice  as  rapidly  as  the  first  and  is  therefore  said  to 
be  twice  as  powerful.    Power  may  be  defined  as  the  rate  of  doing 
work.    It  would  ordinarily,  therefore,  be  measured  in  foot-pounds 
per  second. 

493.  Horse-Power. — About  one  hundred  and  fifty  years  ago, 
the  mine  owners  in  Cornwall  employed  horses  to  operate  the  pumps 
which  kept  their  mines  free  from  water.   As  the  mines  sunk  deeper, 
the  difficulty  and  expense  of  removing  the  water  increased  so  that 
many  were  abandoned  as  no  longer  profitable.     It  was  at  this 
time  that  Watt  perfected  his  steam  engine  and  began  to  introduce 
it  in  the  mines.    The  miners  knew  how  many  horses  were  required 
to  lift  so  much  water  but  had  no  notion  of  the  capabilities  of  the 
new-fangled  engine;  they  therefore  required  that  before  purchas- 
ing an  engine  they  should  be  told  how  many  horses  it  could  sup- 
plant.    In  order  to  be  able  to  furnish  this  information,  Watt 
carried  out  a  series  of  tests  with  the  powerful  horses  used  in  the 
London  breweries,  as  a  result  of  which  he  concluded  that  such  a 
horse  working  eight  hours  a  day  could  perform  work  at  a  rate 
equivalent  to  raising  33,000  pounds  one  foot  per  minute.    This 
figure  has  ever  since  been  accepted  as  the  measure  of  a  horse-power. 
The  unit  of  time  is,  however,  commonly  taken  as  one  second,  the 
corresponding  foot-pounds  being  550. 

In  electrical  measurements,  it  is  desirable  to  express  this  in 
absolute  units.  Remembering  that  the  pound  is  about  445,000 
dynes  (Par.  11),  and  that  the  foot  =30.48  centimeters,  the  horse- 
power is  in  round  numbers  7,460,000,000  (or  746  XlO7)  ergs  per 
second. 

494.  Expression  for  Electric  Power. — There  are  a  number  of 
ways  in  which  an  expression  for  electric  power  may  be  deduced. 


388  ELEMENTS  OF  ELECTRICITY. 

It  is  superfluous  to  say  that  in  every  case  the  results  must  be  the 
same,  yet,  several  of  these  methods  will  now  be  explained,  for  each 
presents  the  matter  from  a  slightly  different  view-point  and  the 
student  will  thus  get  a  broader  grasp  of  the  subject.  We  shall 
begin  with  the  simplest. 

(a)  In  Par.  477  we  saw  that  the  heat  developed  by  a  current  of 
strength  /  flowing  for  t  seconds  through  a  resistance  R  is  I2Rt. 
This  represents  energy  expended,  or  work,  and  if  divided  by  t  it 
will  give  the  rate  at  which  the  work  is  done,  or  the  power  (Par. 
492).    Hence,  the  power  developed  by  a  current  I  in  heating  a 
resistance  R  is  PR. 

This  last  expression  may  be  factored  as  follows:  I2R  =  Ix!R. 
But  IR  is  the  drop  of  potential  E  between  the  two  points  A  and  B 
(Fig.  234),  hence  for  I2R  we  may  write  IE,  or  the  power  expended 
in  heating  any  portion  of  an  electric  circuit  is  measured  by  the 
product  of  the  current  flowing  in  the  circuit  by  the  difference  in 
potential  between  the  ends  of  the  portion. 

(b)  In  Par.  358  it  was  proven  that  the  work  done  by  a  current 
I  flowing  around  a  coil  is  I N,  N  being  the  change  in  the  number 
of  lines  of  force  embraced  by  the  coil.    If  this  work  be  done  in  time 
t,  the  power  =  IN/t.    But  (Par.  425)  N/t  =  E,  and  the  foregoing 
expression  also  reduces  to  IE,  or,  as  above,  the  power  developed  in 
a  coil,  a  portion  of  a  circuit,  is  measured  by  the  product  of  the  cur- 
rent flowing  through  the  circuit  by  the  difference  in  potential 
between  the  ends  of  the  coil.    In  this  case,  the  heating  effect  is 
not  considered. 

(c)  Finally,  taking  the  most  general  case  of  a  portion  of  a  circuit 
of  any  shape  whatsoever,  and  placing  no  restriction  upon  the 
nature  of  the  work  performed  by  the  current,  if  E  be  the  difference 
of  potential  between  the  ends  of  the  portion  and  if  during  the  time 
under  consideration  Q  units  are  transferred  around  the  circuit,  the 
work  done  in  the  portion  is QE  (Par.  72).    But  Q  =  lxt,  hence  the 
work  is  I.  t.  E.    Dividing  this  by  t  to  obtain  the  power,  we  again 
arrive  at  IE,  or,  in  general,  the  power  expended  in  any  portion  of 
an  electric  circuit  is  measured  by  the  product  of  the  current  by  the 
difference  in  potential  between  the  ends  of  the  portion. 

495.  Development  of  Power  in  a  Battery.— Since  the  source  of 
the  energy  developed  in  a  single  cell  is  the  chemical  action  result- 
ing in  the  consumption  of  the  zinc  by  the  acid  (Par.  192),  no  matter 


ELECTRO-MAGNETICS.  389 

how  a  battery  may  be  grouped,  if  the  same  amount  of  zinc  be  con- 
sumed in  the  same  time,  the  same  power  is  developed.  This  may 
be  illustrated  as  follows:  Suppose  N  cells,  each  of  an  E.  M.  F.  of 
e  volts  and  an  internal  resistance  of  r  ohms  be  grouped  in  series 
with  an  external  circuit  of  negligible  resistance.  The  E.  M.  F.  of 
the  battery  is  Ne,  the  current  is  Ne/  Nr  =  e/r,  and  if  z  be  the  zinc 
consumed  in  one  cell  per  second,  the  total  amount  consumed  per 
second  is  Nz. 

If  these  same  cells  be  grouped  in  parallel,  the  E.  M.  F.  of  the 
battery  is  e,  the  current  through  each  cell  is  e/r,  the  total  current 
is  Ne/r  and  the  total  consumption  of  zinc  per  second  is  again  Nz. 
The  power  developed  in  the  two  groupings  should  therefore  be  the 
same.  In  the  first  case  it  is  NeXe/r  or  Ne2/r;  in  the  second  case 
it  is  e  X  Ne/r  or  again  Ne2/r. 

496.  Units  of  Electrical  Power. — From  Par.  494  the  expression 
for  electrical  power  is 

P  =  IE 

If  in  this,  /  be  one  absolute  unit  of  current  and  E  be  one  absolute 
unit  of  E.  M.  F.,  P  becomes  one  absolute  unit  of  electric  power. 
This  unit  has  received  no  name  but  represents  the  expenditure  of 
energy  at  the  rate  of  one  erg  per  second. 

If  in  the  same  expression,  we  make  /  one  ampere  and  E  one 
volt,  we  again  have  P  =  1.  This  unit,  the  practical  unit  of  electric 
power,  is  called  the  watt.  Since  the  ampere  is  1(H  absolute  units 
of  current  and  the  volt  is  108  absolute  units  of  E.  M.  F.  (Par.  427), 
the  watt=  IE=  10 -*X  108  =  107  absolute  units  of  power,  or  ten 
million  ergs  per  second. 

We  saw  in  Par.  493  that  the  horse-power  was  746  XlO7  ergs  per 
second.  The  horse-power  is  therefore  746  watts.  The  commercial 
unit  of  electric  power  is  the  kilowatt,  or  one  thousand  watts.  The 
kilowatt  is  1000/746,  or  just  about  Ij  horse-power.  The  com- 
mercial unit  of  electric  work,  the  unit  by  which  it  is  bought  and 
sold,  is  the  kilowatt-hour. 

497.  Measurement  of  Electric  Power. — Since  the  power  ex- 
pended between  two  points  in  an  electric  circuit  is  measured  by  the 
product  of  the  current  by  the  difference  in  potential  between  the 
two  points,  we  may  measure  the  current  by  an  ammeter,  and 
the  difference  of  potential  by  a  voltmeter,  and  by  multiplication 
obtain  the  watts.   As  an  illustration,  suppose  we  wish  to  determine 


390  ELEMENTS  OF  ELECTRICITY. 

the  consumption  of  power  in  the  16  candle-power,  100  volt  lamp, 
AB,  Fig.  239.  Connections  are  made  as  shown.  The  ammeter 
reads  the  current  /  flowing  through  AB,  and  the  voltmeter  reads 
the  difference  of  potential  E  between  A  and  B.  The  product  of 
these  two  readings  gives  the  watts  consumed.  If,  for  example, 
the  current  be  one-half  ampere  and  the  difference  of  potential 
between  A  and  B  be  100  volts,  the  power  is  50  watts.  It  requires, 


AM 


Fig.  239. 

therefore,  a  kilowatt  to  run  20  such  lamps,  or  about  one  horse- 
power to  run  15. 

If,  in  the  above  example,  the  ammeter  be  read  while  the  volt- 
meter is  connected  up,  a  slight  error  will  be  committed,  for  exami- 
nation of  the  figure  will  show  that  the  ammeter  reads  not  the 
current  through  the  lamp  but  the  sum  of  the  currents  through 
both  the  lamp  and  the  voltmeter.  If  the  resistance  of  the  volt- 
meter be  15,000  ohms  (Par.  458),  the  current  through  it  is  TM§<r 
or  T^  ampere.  The  current  through  the  lamp  is  therefore  really 
i  —  Tfcff  =  ^  ampere,  and  the  power  consumed  in  the  lamp  is 
100  X  T7sV  =  49-J-  watts  instead  of  50,  indicating  an  error  of  1^  per 
cent.  This  may  be  reduced  by  connecting  the  voltmeter,  as  shown 
by  the  dotted  line  D,  in  shunt  with  both  the  lamp  and  the  am- 
meter, or  by  reading  the  ammeter  before  the  voltmeter  circuit  is 
closed.  In  a  similar  manner  it  may  be  shown  that  if  the  current 
be  large  and  the  difference  of  potential  between  A  and  B  be  small, 
the  connection  as  shown  in  the  figure  is  the  best. 

The  determination  of  power  from  the  reading  of  two  separate 
instruments  does  not  give  correct  results  when  applied  to  alternat- 
ing current  circuits.  This  fact  cannot  be  explained  until  the 
subject  of  alternating  currents  is  reached. 


ELECTRO-MAGNETICS. 


391 


498.  Measurement  of  Power  by  Electro-Dynamometer. — By 

making  a  slight  change  in  the  connections  of  an  electro-dynamom- 
eter, it  is  possible  to  use  that  instrument  to  measure  electric 
power.  For  example,  suppose  we  wish  to  measure  the  power  ex- 
pended in  an  incandescent  lamp.  Connections  are  made  as  shown 


Fig.  240. 


diagrammatically  in  Fig.  240.  F  represents  the  heavy  wire  fixed- 
coil  of  a  Siemen's  electro-dynamometer  (see  Fig.  171).  The  end 
of  this  coil  connected  to  the  terminal  A  is  left  undisturbed.  The 
other  end,  which  was  fastened  to  the  metal  bracket  at  D,  is  discon- 
nected and  attached  to  G,  one  terminal  of  the  lamp.  The  main 
current  now  enters  at  H,  passes  through  the  lamp  and  the  coil  F 
and  out  by  A.  A  current  is  shunted  off  at  H,  passes  through  a 
resistance  R  of  several  thousand  ohms,  thence  to  the  terminal  (7, 
thence  around  the  movable  coil  M  to  the  bracket  D  and  finally 
reunites  with  the  main  current  at  G. 

In  Par.  383  it  was  shown  that  the  force  exerted  between  the  two 
coils  carrying  currents  is     f=KIIf 

K  being  a  constant  and  / 

and  I'  being  the  currents  in  the  respective  coils.  If  E  be  the  dif- 
ference of  potential  between  H  and  G,  and  if  R  be  the  resistance 
of  the  shunt  circuit  HRCMDG,  then  the  current  through  the 
movable  coil  is  I'  =  E/R.  Substituting  this  for  I'  in  the  expres- 
sion above,  we  have  -^ 


whence,  since  K  and  R  are 


392 


ELEMENTS  OF  ELECTRICITY. 


constants,  we  see  that  the  force  exerted  between  the  two  coils  of 
the  instrument  is  proportional  to  IE,  the  watts  consumed  between 
H  and  G.  In  the  same  paragraph  it  is  shown  that  this  force  is 
proportional  to  the  angle  of  torsion,  that  is,  to  the  angle  through 
which  the  milled  head  of  the  dynamometer  is  turned  in  order  to 
bring  the  pointer  of  the  movable  coil  back  to  the  zero,  whence  the 
wattage  between  the  points  H  and  G  is  also  proportional  to  this 
angle. 

As  pointed  out  in  Par.  497,  an  error  is  committed  in  this  meas- 
urement unless  the  shunt  current  (the  voltage  current)  be  so  small 
as  to  be  negligible.  On  this  account,  the  resistance  R  is  made  very 
large. 

499.  Indicating  Wattmeter. — Instruments  from  which  may  be 
read  direct  the  power  developed  between  two  points  in  a  circuit 


Fig.  241. 

are  called  wattmeters.  They  are  of  two  general  classes,  the  first 
giving  the  value  of  the  power  at  any  instant  and  called  indicating 
wattmeters;  the  second  summing  up  or  integrating  these  instan- 
taneous values  and  called  integrating  wattmeters. 

Indicating  wattmeters  operate  on  the  principle  of  the  electro- 
dynamometer  described  in  the  preceding  paragraph,  but  are  usual- 
ly so  arranged  as  to  avoid  the  errors  pointed  out  in  Par.  497.  Fig. 
241  represents  the  external  appearance  of  the  Weston  wattmeter. 
Across  the  top  there  are  three  terminals,  the  outer  ones  being  used 


ELECTRO-MAGNETICS. 


393 


for  the  voltage  current  and  one  of  them  being  marked  -f .  The 
central  terminal  is  used  in  a  certain  process  of  calibration,  not 
necessary  to  describe  here.  On  the  left  side  are  the  two  terminals 
for  the  main  current,  one  of  these  also  being  marked  +.  At  the 
bottom  is  a  button  switch  which  closes  the  voltage  circuit.  This 
instrument  may  be  used  with  either  direct  or  alternating  currents. 
When  in  use,  if  the  main  current  be  brought  in  at  the  plus  terminal, 
the  voltage  current  must  enter  by  the  plus  terminal  of  the  top 
row;  if  the  main  current  be  brought  in  at  the  negative  terminal 
the  voltage  current  must  enter  by  the  negative  terminal  of  the 
top  row. 

The  internal  arrangement  of  the  instrument  is  quite  similar  to 
that  of  the  D.  C.  A.  C.  voltmeter  as  described  and  figured  in  Par. 
470.  Fig.  242  represents  diagrammatically  the  connections  made 


Fig.  242. 

to  read  the  power  consumed  in  two  incandescent  lamps  in  series. 
The  main  current  enters  at  A,  passes  around  the  two  fixed  coils 
in  the  direction  shown  by  the  heavy  arrows,  and  leaves  by  B.  It 
does  not  pass  through  the  movable  coil.  The  voltage  current  is 
shunted  off  at  C,  enters  at  D,  passes  through  the  large  resistance 
R,  which  is  wrapped  so  as  to  be  free  from  inductance,  thence  to 
the  movable  coil  around  which  it  flows  as  shown  by  the  broken 
arrow,  then  around  the  fixed  coils  but  opposite  in  direction  to  the 
main  current,  thence  out  by  E,  and  rejoins  the  main  current  at  F. 


394  ELEMENTS  OF  ELECTRICITY. 

The  current  through  the  fixed  coils,  as  has  already  been  pointed 
out  (Par.  497),  is  greater  than  the  current  through  the  lamps 
since  it  consists  of  that  current  plus  the  shunt  current.  To 
correct  for  this,  the  shunt  current  is  carried  around  the  fixed  coils 
in  opposite  direction  to  and  making  as  many  turns  as  the  main 
current. 

500.  Integrating  Wattmeter. — A  consumer  of  electrical  power  is 
charged  on  an  equitable  basis  when  he  pays  in  proportion  to  the 
work  performed  for  him  by  the  current.    He  must  therefore  pay, 
not  for  the  power  alone,  but  for  the  product  of  the  power  and  the 
time  during  which  it  has  been  supplied,  for  since  power  is  the 
rate  of  doing  work  =  w/t  (Par.  492),  work  is  equal  to  power  X  time. 
Electrical  power  is  therefore  sold  not  by  the  watt,  but  by  the  watt- 
hour,  or  more  usually  by  the  kilowatt-hour  (Par.  496).      The 
wattmeter  described  in  the  preceding  paragraph  indicates  the 
instantaneous  values  of  the  power  but  takes  no  account  of  the 
time  element.    Instruments  which  sum  up  the  successive  amounts 
of  work  performed  by  the  current  are  called  integrating  wattmeters. 
Their  principle  is  simple  but  can  not  be  fully  explained  at  this 
point.    One  form  consists  of  a  coil  which  revolves  continuously 
as  long  as  the  current  flows  through  it,  the  rate  of  revolution 
at  any  instant  varying  directly  with  the  power,  and  therefore 
the  total  number  of  revolutions  varying  with  the  total  amount  of 
work  performed.    These  revolutions  are  recorded  by  an  arrange- 
ment like  that  used  in  cyclometers  but  the  dials  are  graduated  to 
read  kilowatt-hours  direct.     The  instrument  is  therefore  anal- 
ogous to  a  gas-meter  which  indicates  at  any  instant  the  total 
amount  of  gas  which  has  flowed  through  it  up  to  that  time  but 
does  not  indicate  the  amount  actually  flowing  through. 

501.  Electrical  Transmission  of  Power. — The  two  prime  sources 
of  power  utilized  at  present  are  water  and  steam.    Of  these,  water 
power  is  much  the  cheaper. 

The  difference  in  level,  upon  which  water  power  largely  depends, 
may  be  natural,  as  in  the  case  of  falls,  or  may  be  artificially 
produced  by  the  erection  of  dams.  In  either  case,  unoccupied 
localities  suitable  for  the  development  of  such  power  are  rapidly 
becoming  scarce.  In  the  immediate  vicinity  of  these  falls  and 
dams,  the  available  sites  for  power  plants  are  usually  restricted. 
By  means  of  shafting,  belting,  cables,  etc.,  the  power  developed 


ELECTRO-MAGNETICS.  395 

by  these  plants  may  be  transmitted  a  few  hundred  feet.  Beyond 
this  limited  zone,  recourse  must  be  had  to  steam  power. 

In  the  majority  of  steam  plants,  coal  is  the  fuel  used  and  this 
has  to  be  transported  from  the  mines  to  the  plants.  On  the  aver- 
age, the  cost  of  transportation  is  greater  than  the  cost  of  the  coal 
itself,  therefore,  steam  plants  located  near  the  mouth  of  a  coal 
mine  have  a  great  advantage  over  those  at  a  distance. 

From  the  foregoing,  the  need  of  a  method  of  cheap  transmission 
of  power  to  a  distance  is  evident.  This  problem  is  solved  by  elec- 
tricity, the  mechanical  power  developed  by  the  plant  being  trans- 
formed into  electrical  power,  sent  out  over  the  line  to  the  desired 
spot  and  there  transformed  back  into  mechanical  power. 

502.  Considerations  Affecting  Electrical  Transmission  of 
Power. — It  was  shown  above  (Par.  494)  that  the  electrical  power 
between  two  points  in  a  circuit  is  measured  by  IE,  the  product 
of  the  current  by  the  difference  of  potential  between  the  points. 
These  two  quantities  may  therefore  vary  reciprocally  and  the  power 
remain  constant.  This  principle  is  of  the  utmost  importance  in 
the  electrical  transmission  of  power.  When  a  current  flows  through 
a  conductor,  a  portion  of  the  power  is  spent  in  heating  the  con- 
ductor, the  power  so  spent  being  PR  (Par.  494),  or  varying  as  the 
square  of  the  current.  To  avoid  this  waste,  the  current  should  be 
kept  as  small  as  possible.  From  what  has  been  shown  above,  we 
can  reduce  the  current  and  still  transmit  the  same  power  pro- 
vided the  voltage  is  varied  inversely  with  the  current.  An  ex- 
ample will  bring  this  out  more  clearly. 

Suppose  an  electric  generator  operated  by  a  water  wheel  is  pro- 
ducing ten  amperes  at  a  pressure  of  two  hundred  volts,  or  develop- 
ing a  power  of  2000  watts,  and  is  transmitting  power  over  a  No.  3, 
B.  and  S.,  copper  wire  to  a  factory  at  a  distance  of  five  miles.  For 
round  numbers,  the  resistance  of  this  wire  may  be  taken  as  one 
ohm  per  mile.  The  PR  loss  due  to  the  resistance  of  the  wire  is 
100  X 10  =  1000  watts,  that  is,  fifty  per  cent  of  the  power  generated 
is  lost  in  the  wire.  If  this  same  generator  turned  out  one  ampere 
at  a  pressure  of  2000  volts,  it  would  still  develop  the  same  power, 
2000  watts,  but  in  this  case  the  I2R  loss  would  be  only  10  watts, 
or  only  one-half  of  one  per  cent  of  the  total  power.  Furthermore, 
if  the  fifty  per  cent  loss  be  permissible,  a  No.  15  wire  may  be  used 
with  the  2000  volt  current  and  the  loss  still  be  kept  within  the 
limit.  Since  the  No.  15  wire  weighs  52  pounds  per  mile  as  com- 


396  ELEMENTS  OF  ELECTRICITY. 

pared  to  838  pounds  for  the  No.  3  wire,  there  would  result  a  saving 
of  7860  pounds  of  copper  costing  about  $1000. 

The  secret  of  electrical  transmission  of  power  to  a  distance  is 
therefore  the  employment  of  high  potential  currents.  As  will  be 
shown  in  Part  V,  high  potential  alternating  currents  are  much 
more  easily  generated  and  transformed  up  and  down  'than  are 
corresponding  direct  currents,  for  which  reasons,  in  the  transmis- 
sion of  power  to  a  distance,  alternating  currents  are  used  almost 
exclusively.  Voltages  as  high  as  20,000  and  30,000  are  frequently 
employed,  and  in  a  few  cases  150,000  has  been  reached  and  power 
has  been  transmitted  upwards  of  three  hundred  miles.  With 
these  very  high  voltages,  the  difficulty  of  obtaining  proper  insu- 
lation for  the  line  increases  greatly.  The  wires  must  be  spaced 
widely  apart  on  the  cross  arms  of  the  poles  and  special  forms  of 
porcelain  insulators  must  be  used.  In  rainy  weather,  the  loss 
from  leakage  becomes  excessive.  Finally,  the  element  of  danger 
to  life  assumes  serious  proportions. 


ELECTRO-MAGNETICS.  397 


CHAPTER  37. 

ELECTRIC   LIGHTING. 

503.  The  Electric  Light.— In  Chapter  35  we  examined  the  heat- 
ing effect  of  the  electric  current.     If  a  body  be  raised  to  a  suf- 
ficiently high  temperature  it  will  emit  light.    The  production  of 
light  by  electricity  is  therefore  only  a  particular  case  of  heating. 

There  are  at  present  three  distinct  classes  of  electric  lights. 
These  are: 

(a)  The  incandescent  lamp.    The  current  is  passed  through  a 
conducting  solid  which  is  raised  to  incandescence.    No  combustion 
takes  place. 

(b)  The  arc  lamp.    The  current  is  passed  across  the  gap  be- 
tween two  electrodes  whose  tips  are  thereby  heated  to  incandes- 
cence.   A  portion  of  one  of  the  electrodes  is  volatilized  and  the 
resulting  vapor  conducts  the  current  across  the  gap.    Combustion 
takes  place,  but  simply  because  air  cannot  be  excluded. 

(c)  The  luminous  vapor  lamp.     The  current  passed  through 
rarefied  gases  or  vapors  contained  in  glass  tubes  causes  these 
vapors  to  glow.    No  combustion  takes  place. 

504.  The  Incandescent  Lamp. — The  incandescent  lamp  does 
not  differ  in  principle  from  the  fuze  described  in  Par.  483.    The 
earlier  forms  consisted  of  a  bare  platinum  wire  which  was  made 
white-hot  by  the  passage  of  the  current.    These  failed  because  the 
platinum  was  necessarily  near  its  melting  point  and  a  slight  in- 
crease in  the  current  would  cause  it  to  give  way;  moreover, 
the  cost  of  the  platinum  was  excessive,  and  for  these  reasons  the 
incandescent  lamp  did  not  become  a  commercial  success  until  the 
development  by  Edison  of  the  carbon  filament.    Carbon  is  infus- 
ible and,  although  a  conductor,  is  a  poor  enough  conductor  to 
permit  the  filaments  to  be  made  of  sufficient  size  for  strength  and 
yet  preserve  the  resistance  required  for  the  development  of  the 
heating  effect.    If,  however,  carbon  be  heated  in  the  presence  of 
oxygen  it  is  soon  consumed.     The  filaments  must  therefore  be 
enclosed  in  a  vacuous  glass  bulb. 


398  ELEMENTS  OF  ELECTRICITY. 

505.  The  Carbon  Filament. — The  first  successful  carbon  fila- 
ments were  made  from  bamboo.    Later  on,  they  were  made  from 
a  compact  paper  which  was  cut  into  thread-like  strips.    They  have 
also  been  made  from  cotton  thread.    They  are  now  manufactured 
from  a  pure  cotton  fibre  which  is  dissolved  into  a  glue-like  liquid 
by  a  solution  of  zinc  chloride.    This  is  forced  through  small  holes 
in  a  die  and  emerges  in  rather  soft  endless  threads,  a  little  over  one- 
fiftieth  of  an  inch  in  diameter,  which  are  caught  in  a  vessel  con- 
taining alcohol.    The  alcohol  dehydrates  and  hardens  the  threads, 
which  are  then  washed  free  of  the  zinc  chloride,  coiled  up  and 
dried.    They  now  resemble  fiddle  strings.    These  are  cut  up  into 
the  proper  length,  given  the  required  shape  by  being  wrapped 
upon  a  form  and  are  then  embedded  in  pulverized  carbon  in  a 
covered  crucible  and  carbonized  at  a  high  temperature.    After 
cooling,  they  are  attached  to  holders,  placed  in  a  vessel  in  which 
they  are  surrounded  by  the  vapor  of  gasoline,  and  heated  white 
hot  by  a  current.    This  process  is  called  "flashing."    The  gasoline 
is  decomposed  and  deposits  a  semi-metallic  film  of  gas  coke  on  the 
filaments.    This  renders  them  stronger,  more  uniform  in  resistance, 
and  of  a  steely  black  color.    The  diameter  has  now  shrunk  to  .0035 
inch. 

An  additional  process  recently  introduced,  consists  in  placing 
the  filaments,  both  before  and  after  flashing,  in  an  electric  furnace 
and  raising  them  to  a  still  higher  temperature  by  which  they  are 
partially  graphitized.  Filaments  so  treated  are  said  to  be  "metal- 
lized," and  their  light-giving  efficiency  is  much  increased. 

506.  Manufacture  of  the  Lamps. — The  current  enters  and  leaves 
the  glass  bulb  through  two  wires  fused  into  a  small  glass  tube  or 
stem  which  is  inserted  into  the  bulb  and  fused  to  it.    The  portion 
of  these  "leading-in  wires"  which  passes  through  the  glass  of  the 
stem  (A  and  B,  Fig.  243)  must  be  of  platinum.    The  coefficients 
of  expansion  of  glass  and  of  platinum  are  about  the  same  and  they 
therefore  expand  and  contract  together.    With  other  metals,  the 
glass  would  either  be  cracked  by  the  greater  expansion  of  the  wire 
or  the  vacuum  would  be  destroyed  by  the  shrinking  of  the  metal 
away  from  the  glass.    Copper  wires  are  fastened  to  the  outer  ends 
of  A  and  B  and  the  filament  is  attached  to  the  other  ends  by  means 
of  a  carbon  paste.    One  of  the  copper  wires  is  soldered  to  the  brass 
shell  which  carries  the  screw  threads  of  the  lamp  base.    The  bot- 
tom of  this  shell  is  closed  by  a  glass  or  porcelain  button  in  the  center 


ELECTRO-MAGNETICS.  399 

of  which  is  a  brass  contact,  pierced  with  a  small  hole.  The  remain- 
ing copper  wire  is  drawn  through  this  hole  and  soldered  to  the 
contact.  The  shell  is  fastened  to  the  bulb  by  a  cement  or  by  plaster 
of  Paris.  Lamp  sockets  are  so  arranged  that  when  a  bulb  is 
screwed  in,  the  required  connections  are  made. 

A  small  tube  is  left  at  E.  This  is  now  attached  to  an  air  pump 
and  most  of  the  air  is  withdrawn  from  the  bulb.  When  a  good 
vacuum  has  been  obtained,  a  current  is  sent  through  the  lamp. 
This  drives  out  the  gases  which  have  been  occluded  in  the  carbon 
filament.  The  last  traces  of  oxygen  are  removed  by  igniting  a 
small  amount  of  phosphorus  inserted  for  that  purpose  at  E,  and 
E  is  then  sealed  by  a  blow-pipe  flame. 


Fig.  243. 

In  lamps  with  long  and  slender  filaments,  the  filaments  are  liable 
to  be  broken  by  excessive  vibration,  or  when  hot  may  droop,  touch 
the  bulb  and  crack  it.  To  remedy  this  they  are  often  supported 
at  their  middle  point  by  a  short  wire,  one  end  of  which  is  fused  into 
the  tip  of  the  glass  stem  on  the  interior  of  the  lamp.  Such  fila- 
ments are  said  to  be  "anchored." 

Incandescent  lamps  are  run  at  constant  voltages.  Since  the 
heating  effect,  on  which  the  light-giving  effect  depends,  varies  as 
PR  =  IE  (Par.  477),  and  since  E  is  constant,  the  lighting  effect  is 
increased  by  increasing  the  current.  This  is  done  by  decreasing 
the  resistance  of  the  lamp,  that  is,  by  making  the  filament  shorter 
and  stouter. 

507.  Recent  Incandescent  Lamps. — As  has  just  been  stated, 
the  light-giving  effect  of  an  incandescent  lamp  increases  with  the 
temperature.  It  is  therefore  desirable  to  heat  the  filament  as 
highly  as  possible.  As  the  temperature  of  the  ordinary  carbon 
filament  increases,  so  does  the  brilliancy  of  the  light  it  emits,  but 
the  life  of  the  lamp  is  very  much  shortened  thereby  and  it  is  not 
found  practicable  to  exceed  a  temperature  of  1350°  C. 


400 


ELEMENTS  OF  ELECTRICITY. 


We  saw  (Par.  504)  that  in  the  early  lamps  attempts  were  made 
to  use  platinum  filaments.  Platinum,  which  fuses  at  1775°  C, 
was  the  most  infusible  metal  which  could  then  be  obtained  yet 
had  to  be  abandoned  because  the  filaments  melted.  There  are 
known,  however,  certain  rare  metals  whose  fusing  points  are  much 
higher  than  that  of  platinum.  Among  these  are  osmium,  tantalum 
and  tungsten,  this  last  fusing  at  3200°  C.  Their  rarity,  the  dif- 
ficulties of  their  metallurgy,  and  their  consequent  cost  prohibited 
their  use.  These  metals  may  now  be  obtained  and  are  success- 
fully used  in  incandescent  lamps.  Their  conductivity  being  so 
much  greater  than  that  of  carbon,  in  order  to  secure  the  necessary 
resistance  they  must  be  drawn  into  extremely  fine  wires.  When 
they  have  been  drawn  down  so  that  they  look  almost  as  slender  as 
a  spider's  web,  their  resistance  is  still  too  small  and  can  be  in- 


Fig.  244. 

creased  only  by  taking  longer  portions  for  filaments,  about  twenty 
inches  on  an  average.  Even  with  this  length,  it  is  stated  that  as 
many  as  20,000  may  be  made  from  a  single  pound  of  tantalum,  and 
this  although  the  specific  gravity  of  tantalum  is  greater  than  that 
of  lead.  To  insert  these  long  filaments  into  the  lamp  bulb,  they 
must  be  folded  back  and  forth  a  number  of  times  and  having  very 
little  rigidity  when  cold  and  becoming  soft  when  heated,  they  must 
be  supported  at  several  points.  The  expansion  and  contraction  of 
a  twenty-inch  filament,  especially  if  it  be  attached  to  supports  at 
intermediate  points,  is  very  liable  to  break  it,  for  which  reason  it 
is  found  better  to  cut  the  filament  into  four  or  five  pieces  and  to 
connect  these  pieces  in  series.  Even  in  this  case,  especial  provi- 
sion must  be  made  to  allow  for  the  expansion  and  contraction. 
Fig.  244  shows  diagrammatically  the  arrangement  of  the  filament 
in  a  tungsten  lamp.  The  leading-in  wires  pass  through  a  glass 
stem  just  as  in  the  carbon  lamp.  To  this  stem  and  in  prolongation 
of  it  there  is  fused  a  slender  glass  rod  expanded  into  a  button  at 


ELECTRO-MAGNETICS.  401 

A  and  at  B,  points  about  two  inches  apart.  Into  the  button  A 
there  are  fused  four  V-shaped  pieces  of  wire,  the  vertices  of  the  V's 
being  embedded  in  the  glass  so  that  the  free  ends  radiate  like  the 
spokes  of  a  wheel.  Into  the  button  B  there  are  fused  five  equi- 
distant straight  pieces  of  wire.  These  are  shorter  than  the  pieces 
in  A,  but  are  brought  out  to  the  same  length  by  an  attached  piece 
of  the  filament  wire,  this  last  terminating  in  a  small  circular  loop. 
A  piece  of  the  filament  is  attached  to  the  terminal  C,  the  free  end 
is  then  threaded  through  the  loop  D  and  brought  back  and  at- 
tached to  E.  A  second  piece  is  attached  to  F,  carried  through  the 
loop  G  and  fastened  to  H,  and  so  on  around  the  axis.  A  develop- 
ment of  these  connections  is  shown  at  the  right  of  Fig.  244,  whence 
it  is  seen  that  the  successive  pieces  of  filament  are  in  series.  The 
flexible  ends  of  those  arms  which  radiate  from  B  allow  for  the  ex- 
pansion and  contraction  of  the  filaments  which  they  support. 
These  lamps  produce  a  very  fine  white  light  with  a  smaller  expendi- 
ture of  energy  than  in  the  case  of  the  carbon  lamp. 

508.  The  Nernst  Lamp. — The  oxides  of  certain  of  the  rarer 
metals,  yttrium,  thorium,  zirconium,  are  infusible  and  if  highly 
heated  emit  a  very  bright  light.  It  is  on  this  account  that  these 
oxides  are  used  in  the  mantles  of  the  Welsbach  burner.  When 
cold,  they  do  not  conduct  electricity  but  if  heated  to  about  700°  C 
they  become  conductors  and  if  a  current  be  now  passed  through 
them  they  may  be  heated  to  a  point  where  they  glow  with  great 
brilliancy.  This  property  is  utilized  in  the  Nernst  lamp.  The 
light  is  emitted  from  a  glower,  a  little  rod  of  these  oxides  about 
two  centimeters  (three-quarters  of  an  inch)  long  and  one  millime- 
ter in  diameter.  The  light-giving  power  of  a  lamp  is  increased  by 
using  more  than  one  glower.  The  lamp  must  be  provided  with 
an  auxiliary  arrangement  by  which  (a)  the  glower  is  heated  up  to 
the  conducting  point  and  (b)  the  current  is  then  switched  from  the 
heater  to  the  glower. 

Fig.  245  shows  diagrammatically  the  operation  of  the  lamp. 
A  is  an  armature,  bent  at  an  angle  and  pivoted  as  shown.  Its 
shape  causes  its  lower  end  to  hang  out  and  make  contact  at  C. 
H  is  the  heater,  a  slender  porcelain  tube  around  which  is  wrapped 
a  coil  of  very  fine  platinum  wire  which,  for  protection,  is  embedded 
in  a  white  cement  paste.  M  is  an  electro-magnet  with  an  L-shaped 
core.  The  current  enters  at  D,  travels  down  A,  passes  through  the 
contact  C,  around  H  and  out  by  E.  The  passage  of  the  current 


402 


ELEMENTS  OF  ELECTRICITY. 


through  H  heats  it  and  in  less  than  half  a  minute  the  glower  G  has 
been  raised  to  a  conducting  temperature.  The  current  entering  at 
D  may  now  pass  around  M,  through  the  resistance  B,  through  G 
and  out.  M  becomes  magnetized,  the  armature  A  is  attracted  and 
the  contact  at  C  is  broken.  The  full  current  now  passes  through  (7. 
Owing  to  the  method  of  operation  of  the  current  shifter,  these 
lamps  are  restricted  to  a  vertical  position. 


Fig.  245. 

As  the  temperature  of  G  rises,  its  resistance  decreases.  This 
would  permit  a  larger  current  to  flow  through  G  and  its  tempera- 
ture would  rise  still  higher,  and  so  on,  until  the  glower  would  be 
melted.  This  rise  of  current,  however,  is  controlled  by  the  resist- 
ance B,  a  fine  iron  wire  which,  to  prevent  oxidation,  is  sealed  up  in 
a  glass  tube  in  an  atmosphere  of  nitrogen.  It  is  adjusted  to  permit 
the  passage  of  the  required  current  at  the  voltage  for  which  the 
lamp  is  intended.  The  resistance  of  iron  increases  rapidly  with 
the  temperature  and  an  increase  of  seven  per  cent  in  the  current 
will  double  the  resistance  of  B.  Variations  in  the  voltage  do  not, 
therefore,  cause  proportional  variations  in  the  current  through  the 
lamp.  A  resistance  such  as  B,  which  steadies  or  prevents  undue 
fluctuations  in  the  current,  is  commonly  called  a  "ballasting  coil" 
or  simply  "ballast." 

Since  the  glower  is  composed  of  oxides,  it  is  not  necessary  to 
seal  it  up  in  a  bulb.  It  is,  however,  usually  surrounded  by  a 
glass  globe.  Doubtless  on  account  of  electrolytic  action,  the 


ELECTRO-MAGNETICS.  403 

life  of  a  glower  is  less  with  direct  current  than  with  alternating 
current. 

509.  Candle-Power. — Lamps  are  rated  according  to  the  in- 
tensity of  the  light  which  they  emit  under  normal  conditions,  as 
4,  8,  10,  16,  32,  50,  and  100  candle-power.    The  British  standard 
candle  is  defined  as  a  spermaceti  candle,  seven-eighths  of  an  inch 
in  diameter,  weighing  one-sixth  of  a  pound,  and  burning  at  the 
rate  of  120  grains  per  hour.    The  German  standard,  the  Hefner 
unit,  or  the  Hefner,  is  the  light  emitted  by  a  lamp  of  prescribed 
dimensions  burning  amyl  acetate.    The  hefner  is  about  .88  of  a 
candle-power.     In  actual  measurements  of  candle-power,  use  is 
made  of  secondary  standards,  incandescent  lamps  whose  candle- 
power  has  been  determined  by  comparison  with  the  primary  units. 
The  standards  in  use  in  this  country  are  determined  from  the 
hefner. 

In  many  electric  lamps,  the  light  emitted  in  certain  directions 
is  greater  than  that  emitted  in  others.  Such  lamps  are  frequently 
rated  according  to  their  mean  spherical  candle-power,  that  is,  the 
candle-power  if  the  total  light  emitted  were  spread  uniformly  over 
the  surface  of  a  sphere  with  the  lamp  as  a  center. 

510.  Photometry. — Measurement  of  candle-power  is  made  by 
photometers.    Various  kinds  of  these  instruments  are  described  in 
detail  in  the  electrical  handbooks.    In  brief,  they  consist  of  an 
arrangement  by  which  a  beam  from  the  standard  falls  side  by  side 
on  a  screen  with  a  beam  from  the  light  being  measured.    One  of 
the  lights  is  shifted  back  and  forth  until  the  illumination  on  the 
adjoining  surfaces  is  the  same.    When  this  equality  of  illumination 
has  been  attained,  then,  since  the  intensity  of  illumination  varies 
inversely  as  the  square  of  the  distance  from  the  source,  the  candle- 
power  of  the  lamps  are  to  each  other  directly  as  the  squares  of 
their  respective  distances  from  the  screen. 

511.  Life  of  Incandescent  Lamp. — The  life  of  an  ordinary  16 
candle-power  incandescent  lamp  may  exceed  2000  hours.    How- 
ever, the  candle-power  of  a  lamp,  although  slightly  above  normal 
for  the  first  fifty  hours,  decreases  steadily  thereafter,  and  it  is  laid 
down  as  a  rule  that  the  smashing  point  of  the  lamp  is  reached  when 
its  candle-power  has  fallen  to  80  per  cent  of  its  rated  value.    This, 
on  an  average,  is  after  about  600  hours'  use.     The  useful  life 
depends  greatly  upon  the  accuracy  with  which  the  voltage  is 


404  ELEMENTS  OF  ELECTRICITY. 

regulated.  It  is  stated  that  an  increase  of  three  per  cent  in  the 
voltage  will  shorten  the  life  of  a  lamp  one-half.  On  the  other  hand, 
a  decrease  of  ten  per  cent  in  the  voltage  reduces  the  candle-power 
47  per  cent. 

512.  Efficiency. — The  efficiency  of  an  incandescent  lamp  should 
be  measured  by  the  light  produced  by  the  expenditure  of  a  certain 
amount  of  power,  that  is,  by  the  candle-power  per  watt.  In  practice  • 
however,  a  custom  the  reverse  of  this  has  arisen  and  the  efficiency 
of  a  lamp  is  given  by  stating  the  number  of  watts  required  to  pro- 
duce one  candle-power.    In  this  case,  the  greater  the  number  of 
watts,  the  less  the  efficiency  of  the  lamp.    The  hot  resistance  of  an 
ordinary  110  volt,  16  candle-power  lamp  is  220  ohms.    The  current 
through  the  lamp  is  therefore  one-half  ampere,  and  the  power  con- 
sumed is  110x1/2=55  watts.    The  wattage  per  candle-power  is 
therefore  55/16  =  3.1.     By  increasing  the  voltage,  more  light  is 
produced  and  the  efficiency  may  be  made  2.7  watts  per  candle- 
power,  but  in  this  case  the  life  of  the  lamp  is  very  much  shortened 
(Par.  511). 

The  efficiency  of  the  Nernst  lamp  is  1.75  watts  per  candle- 
power  and  that  of  the  tungsten  lamp  is  1.5  watts  or  even  less. 

513.  Control  of  Light. — An  objection  to  the  incandescent  lamp 
is  that  it  can  not  easily  be  turned  down.    We  shall  see  later  that 
if  a  large  number  of  closely-grouped  lamps,  such  as  are  used  in 
illuminating  the  stage  of  a  theatre,  be  run  by  alternating  cur- 
rent, it  is  possible  to  turn  them  down  simultaneously  by  a  simple 
piece  of  apparatus  (Par.  621),  but  it  is  not  practicable  to  apply 
this  to  individual  lamps.     It  is  theoretically  possible  to  insert 
in  series  with  a  lamp  a  variable  resistance,  a  rheostat  (Par.  302), 
by  which  the  current,  and  consequently  the  light,  may  be  con- 
trolled, but  the  cost  and  the  necessary  bulk  of  such  arrangement 
prohibit  its  use. 

514.  Grouping   of   Incandescent    Lamps. — Assuming   that   in 
transmitting  electrical  power  from  the  generator  to  the  spot  where 
the  power  is  to  be  used  the  principles  outlined  in  Par.  502  have 
been  observed,  in  utilizing  this  power  for  purposes  of  illumination, 
the  lamps  may  be  grouped  either  in  series  or  in  parallel,  though  the 
latter  arrangement  is  by  far  the  commoner  of  the  two.    Among 
the  considerations  which  lead  to  the  selection  of  one  grouping 
in  preference  to  the  other,  the  principal  are  the  distances  by  which 


ELECTRO-MAGNETICS.  405 

the  individual  lamps  are  separated  and  the  nature  of  the  current, 
whether  direct  or  alternating. 

If  the  lamps  are  to  be  located  close  together,  as  in  the  illumina- 
tion of  the  rooms  of  a  building,  the  parallel  arrangement  should  be 
followed.  A  striking  advantage  of  this  arrangement  is  the  in- 
dependence of  the  several  lamps  and  the  automatic  adjustment 
of  the  current  to  suit  the  demands  made  upon  it.  The  following 
will  make  this  clear. 

In  Fig.  246,  G  represents  a  generator  constructed,  as  will  be  ex- 
plained in  Part  V,  so  as  to  maintain  a  constant  difference  of  poten- 


Fig.  246. 

tial  between  the  mains  A  and  B.  L  represents  a  number  of  lamps 
arranged  in  parallel  -between  these  mains.  Suppose  the  resistance 
of  a  lamp  to  be  220  ohms,  and  the  difference  of  potential  between 
A  and  B  to  be  110  volts.  If  one  lamp  be  turned  on,  the  current 
through  it  will  be  /  =  E/R  =  110/220  =  1/2  ampere.  If  four  lamps 
be  turned  on,  the  resistance  between  A  and  B  is  reduced  to  220/4 
=  55  ohms  and  the  current  is  now  110/55=2  amperes,  but  since 
there  are  four  paths,  one-fourth  of  the  total  current,  or  one-half 
ampere,  flows  through  each  so  that  each  lamp  gets  its  proper  cur- 
rent. So  long  as  the  difference  of  potential  between  A  and  B  is 
maintained,  each  lamp  when  turned  on  will  receive  its  proper 
current,  and  whether  it  be  turned  off  or  on  will  not  interfere  with 
the  remaining  lamps. 

There  are  still  other  parallel  arrangements,  such  as  the  three- 
wire  system,  the  five- wire  system,  etc.,  in  which  more  than  two 
mains  are  used,  but  explanation  of  these  is  deferred  until  the 
machines  supplying  the  currents  for  these  systems  have  been 
described. 

If  the  lamps  are  to  be  widely  scattered,  as  in  street  illumination, 
they  should  be  arranged  in  series  and  supplied  by  a  constant  current 
generator.  At  the  Military  Academy  the  roads  are  lighted  by 
incandescent  lamps,  each  requiring  three  amperes  at  50  volts,  and 
arranged  in  series,  50  in  a  circuit.  The  generator  must,  therefore, 
supply  three  amperes  at  a  pressure  of  2500  volts.  Were  these 


406 


ELEMENTS  OF  ELECTRICITY. 


lamps  arranged  in  parallel,  the  mains  would  have  to  carry,  for  a 
portion  of  their  length  at  least,  a  current  of  150  amperes. 
Since  the  lamps  are  in  series,  should  one  burn  out,  the  remainder 
would  ordinarily  be  extinguished.  To  avoid 
this,  an  arrangement  shown  diagrammatically 
in  Fig.  247  is  employed.  From  the  lamp  socket 
proper  there  extend  downward  two  brass 
springs  C  and  D,  shaped  so  that  they  press 
tightly  together  like  a  pair  of  spring  tweezers. 
They  are  kept  from  actual  contact  by  a  thin 
sheet  E  of  mica,  or  of  similar  insulating  ma- 
terial, which  is  inserted  between  them.  When 
in  position,  these  upper  springs  make  contact 
with  corresponding  springs  A  and  B,  by  which 
the  current  is  brought  in  and  taken  out.  Should 
the  lamp  burn  out,  breaking  the  circuit,  the 
voltage  between  C  and  D,  which  up  to  this  time 
had  been  50,  immediately  mounts  to  2500.  This 
is  sufficient  to  pierce  the  sheet  of  mica  E,  burn 
Fig.  247.  it  out,  and  re-establish  the  circuit. 

515.  The  Arc  Lamp. — The  electric  arc  was  described  in  Par.  485 
and  later  its  use  in  the  electric  furnace  was  explained.    It  was  also 
pointed  out  that  not  until  the  comparatively  recent  development 
of  machinery  for  supplying  the  necessary  current  did  it  become 
possible  to  utilize  it.    It  was  discovered  by  Davy  in  1808.    By 
means  of  a  battery  of  2000  cells  and  with  charcoal  electrodes  he 
produced  an  arc  four  inches  long  and  of  very  great  brilliancy. 
Thirty-five  years  later  Foucault  substituted  the  more  compact  gas 
coke  for  the  charcoal  used  by  Davy.    Carbon  is  still  the  principal 
material  used,  although  certain  other  substances  have  recently 
been  introduced  (Par.  523). 

Arc  lamps  may  be  grouped  in  series  or  in  parallel,  the  same  con- 
siderations governing  as  explained  in  the  preceding  paragraph. 
Since  they  are  most  largely  used  for  external  illumination,  and 
also  since  they  require  a  much  larger  current  than  does  the  incan- 
descent lamp,  they  are  usually  arranged  in  series. 

516.  The  Carbons. — The  carbons  for  use  in  the  arc  lights  are 
made  with  the  greatest  care.    They  are  made  from  lampblack,  or 
from  gas  coke,  or  from  a  similar  coke  produced  in  refining  certain 


ELECTRO-MAGNETICS.  407 

petroleum  products.  These  forms  of  carbon  are  ground  to  a  very 
fine  powder,  passed  through  a  bolting  cloth  like  that  used  in  the 
manufacture  of  flour,  and  intimately  mixed  with  granulated  pitch 
which  is  warmed  enough  to  cause  the  ingredients  to  adhere.  The 
mixture  is  then  cooled  and  again  ground  to  a  fine  powder  and 
passed  through  the  bolting  cloth.  The  resulting  meal  is  formed 
into  rods,  either  by  being  compressed  between  steel  molds  by 
hydraulic  pressure  or  by  being  forced  through  a  die  and  emerging 
in  a  continuous  piece  which  is  cut  up  into  the  required  lengths. 
The  rods  are  then  placed  in  layers  in  a  furnace,  the  layers  being 
separated  and  covered  by  sand,  and  they  are  then  heated  and 
maintained  at  a  high  temperature  for  from  ten  days  to  two  weeks. 
In  this  process  a  good  many  are  spoiled  by  warping.  The  carbons 
thus  prepared  are  frequently  copper-plated.  The  coating  of  cop- 
per strengthens  the  rods,  prevents  chipping  and  the  formation  of 
dust,  and  adds  about  one-fifth  to  the  life  of  the  carbon,  but  its 
main  object  is  to  obtain  a  better  electrical  contact.  The  molded 
carbons  are  the  most  largely  used  but,  mainly  because  of  the  re- 
mains of  the  web  along  the  sides,  they  are  not  exactly  cylindrical 
and  can  not  be  used  in  certain  forms  of  arc  lamps  described  later 
(Par.  521).  The  pressed  carbons  are  perfectly  cylindrical  and 
when  necessary  can  also  be  made  in  the  form  of  a  tube  for  the 
manufacture  of  cored  carbons.  The  average  arc  light  carbons  are 
one-half  inch  in  diameter  and  vary  from  six  to  twelve  or  more 
inches  in  length.  Their  average  resistance  is  0.15  ohm  per  foot. 
Carbons  for  search  lights  may  be  as  much  as  two  inches  in  diam- 
eter. 

517.  Requirements  of  Arc  Lamp  Mechanism. — The  mechanism 
of  an  arc  lamp  must  automatically  perform  the  following  functions: 

(a)  When  the  current  is  turned  on,  it  must  bring  the  carbons 
into  contact. 

(b)  It  must  then  "strike"  the  arc  by  separating  the  carbons  the 
proper  distance. 

(c)  As  the  carbons  consume  away,  it  must  feed  them  together. 

(d)  If  the  carbons  approach  too  close,  it  must  separate  them. 

(e)  If  the  arc  goes  out  it  must  restrike  it. 

(f )  In  a  series  arrangement,  if  the  carbon  burns  out  or  breaks, 
a  cut-out  switch  must  operate  to  shunt  the  current  by  the  dis- 
abled lamp. 


408 


ELEMENTS  OF  ELECTRICITY. 


When  it  is  realized  that  the  mechanical  and  electrical  arrange- 
ments by  which  the  foregoing  objects  are  attained  must  differ 
according  as  the  lamps  are  connected  in  series  or  in  parallel,  and 
also  must  differ  according  as  direct  or  alternating  current  is  to  be 
used,  it  will  be  seen  that  the  kinds  of  lamps  are  very  numerous. 
We  can  do  no  more,  therefore,  than  outline  the  principle  of  opera- 
tion of  a  few  typical  forms. 

518.  The  Clutch. — In  all  ordinary  direct  current  arc  lamps,  the 
positive  carbon  is  the  upper  one.  There  are  two  reasons  for  this. 
The  first  and  principal  is  because  eighty-five  per  cent  of  the  light 
produced  by  the  arc  is  emitted  from  the  crater  at  the  tip  of  the 
positive  carbon  and  therefore  this  must  be  above  so  as  to  throw 
its  illumination  downwards.  The  second  is  because  the  positive 
carbon  is  consumed  more  than  twice  as  rapidly  as  the  negative,  or 
in  open  arcs  at  the  rate  of  about  one  and  a  half  inches  per  hour 
and  by  placing  it  above  it  is  in  the  best  position  to  be  fed  by  grav- 
ity. These  considerations  do  not  apply  to  alternating  current 
lamps,  nor  to  certain  projectors  and  search  lights.  In  this  last 
class  it  is  desirable  that  the  crater  should  face 
the  reflector  and  lie  in  its  focus;  the  carbons  are 
accordingly  often  placed  horizontally,  or  one 
horizontal  and  the  other  vertical,  and  both  may 
be  fed  automatically  or  by  hand.  The  arrange- 
ment by  which  the  upper  carbon  is  lifted  and 
held  at  the  proper  distance  from  the  lower 
and  by  which  it  is  allowed  to  slide  down  as 
it  burns  away,  is  called  the  clutch.  There  are 
many  forms  of  clutches.  Some  operate  like  the 
tongs  used  in  hoisting  stones  and  close  when 
they  are  raised  but  open  when  they  are  lowered. 
^^^^  A  very  simple  form  is  shown  in  section  in  Fig. 

248.    This  consists  of  a  metal  plate  A  pierced 
I      I  with  a  circular  hole  slightly  larger  in  diameter 

^— '  than  the  carbon  holder  which  passes  through  it. 

One  end  of  this  plate  fits  loosely  in  the  jaws  B 


III    I 


Fi    248 


of  the  lifting  apparatus.  As  B  rises,  the  plate  A  is  canted  and 
thus  grasps  the  rod.  When  B  is  lowered,  A  strikes  the  stop  C 
and  is  brought  to  a  horizontal  position,  thus  releasing  the  carbon 
which  slips  down. 


ELECTRO-MAGNETICS. 


409 


519.  Constant  Potential  Arc  Lamp. — As  stated  above,  arc  lamps 
may  be  run  in  series  or  in  parallel.    The  series  arrangement  is  by 
far  the  more  common,  but  the  parallel  grouping  is  also  frequently 
employed,  especially  for  interior 

illumination.  In  this  case  the 
lamps  are  connected  across  mains 
between  which  a  constant  differ- 
ence of  potential  is  maintained. 
One  of  these  lamps  is  shown  dia- 
grammatically  in  Fig.  249.  With 
the  carbons  in  contact,  when  the 
switch  S  is  closed  the  current 
enters  at  A,  passes  through  the 
resistance  R,  thence  through  the 
solenoid  C  to  the  upper  carbon, 
down  this  to  the  lower  carbon  and 
out  by  B.  The  current  passing 
through  C  causes  it  to  suck  up  the 
plunger  and,  through  the  clutch, 
to  raise  the  upper  carbon  and  thus 
strike  the  arc.  As  the  carbons 
burn  away,  the  arc  gets  longer 
and  its  resistance  increases.  This 
reduces  the  current,  and  the  lift- 
ing power  of  C  grows  less  until  finally  it  can  no  longer  support 
the  plunger  and  the  carbon  and  they  fall.  The  clutch  strikes  the 
stop  and  releases  the  carbon  which  slides  down,  shortening  the 
arc.  This  increases  the  current  and  the  plunger  is  again  drawn 
up,  and  so  on. 

Without  the  resistance  R,  the  result  of  closing  the  switch  with 
the  carbons  in  contact  would  be  in  the  nature  of  a  short  circuit 
(Par.  306).  This  resistance  steadies  the  current  by  preventing 
violent  fluctuations  and  it  is  therefore  a  "ballast"  as  described  in 
Par.  508. 

520.  Constant  Current  Arc  Lamp. — For  operating  arc  lamps 
in  series,  the  generator  and  its  regulator  are  designed  so  as  to 
furnish  a  constant  current,  therefore,  whether  the  arc  be  long 
or  short  the  current  is  the  same.    On  this  account,  resistance  in 
series  with  the  lamp  is  not  required.     Furthermore,  the  arrange- 
ment described  in  the  preceding  paragraph  could  not  be  used,  for 


Fig.  249. 


410 


ELEMENTS  OF  ELECTRICITY. 


the  pull  of  the  solenoid  upon  its  plunger  being  constant,  the 
carbon  would  not  feed.  For  such  lamps  the  so-called  "differen- 
tial" mechanism  is  employed.  This  is 
shown  diagrammatically  in  Fig.  250. 
With  the  carbons  in  contact,  the  open- 
ing of  the  switch  S  causes  the  current 
entering  at  A  to  pass  around  the  sole- 
noid to  the  point  C,  thence  to  the  upper 
carbon,  thence  to  the  lower  and  out  by 
B.  The  passage  of  this  current  actuates 
the  clutch  and  strikes  the  arc.  To 
cause  the  carbon  to  feed,  a  differential 
coil  is  taken  off  at  the  point  C  and  con- 
nected at  D,  that  is,  it  is  in  shunt  with 
the  arc.  This  coil  is  of  many  turns  of 
fine  wire  and  is  wrapped  in  opposite 
direction  to,  and  inside  of  the  first,  but 
for  clearness  is  represented  in  the  dia- 
gram as  being  below.  The  two  coils 
being  wrapped  in  opposite  directions, 
the  pull  upon  the  solenoid  plunger  is 
due  to  the  difference  of  the  ampere 

turns  in  the  two.  With  the  carbons  in  contact,  the  difference  of 
potential  between  E  and  D  is  very  little,  therefore,  a  very 
small  current  flows  through  the  differential  coil.  As  the  car- 
bons draw  farther  and  farther  apart,  the  resistance,  and 
consequently  the  difference  of  potential,  between  E  and  D  in- 
creases. This  causes  an  increasing  current  to  flow  through  the 
differential  coil  and  weakens  more  and  more  the  pull  on  the 
plunger.  A  point  is  finally  reached  when  the  plunger  drops  and 
the  carbon  feeds. 

521.  The  Enclosed  Arc. — The  wasting  away  of  the  carbons  in 
the  ordinary  arc  lamp  is  mainly  due  to  the  combination  of  the 
white  hot  carbon  vapor  with  the  oxygen  of  the  air.  It  is  not 
practicable  to  enclose  the  carbons  in  air-tight  globes  but  in  recent 
years  there  has  been  introduced  a  form  of  arc  lamp  in  which  the 
arc  is  surrounded  by  a  globe  so  fitted  that  the  admission  of  air  is 
reduced  to  a  minimum,  and  in  these  the  life  of  the  carbons  is  very 
greatly  prolonged,  the  consumption  being  reduced  from  1.5  inches 
per  hour  to  less  than  one-tenth  of  an  inch.  In  addition  to  the  sav- 


ELECTRO-MAGNETICS.  411 

ing  in  carbons,  there  is  a  very  great  saving  in  labor  since  the  lamps, 
instead  of  having  to  be  "trimmed"  or  supplied  with  fresh  carbons 
daily,  average  over  100  hours  and  may  be  run  as  long  as  200  hours 
without  attention.  Other  advantages  are  a  steadier  light  and 
absence  of  the  hissing  noise  of  the  open  arcs.  The  principal  chan- 
nel for  the  admission  of  air  to  the  arc  is  the  space  around  the  carbon 
since  this  latter  must  be  free  to  be  moved  by  the  lamp  mechanism. 
To  reduce  this,  the  carbons  must  fit  the  opening  very  accurately, 
for  which  reason,  as  already  mentioned  (Par.  516),  pressed  car- 
bons are  used  instead  of  the  molded. 

522.  The  Flaming  Arc. — With  the  common  arc  light,  the  carbons 
are  from  one-sixteenth  to  less  than  a  quarter  of  an  inch  apart  and 
the  greater  part  of  the  light  is  emitted  from  the  incandescent  car- 
bons, although  the  maximum  heat  is  developed  within  the  arc 
itself  (Par.  485).  If  it  were  possible  to  suspend  within  this  arc 
a  non-combustible  solid,  like  the  mantle  of  the  Welsbach  burner, 
it  would  be  heated  to  incandescence  and  the  heat  energy  of 
the  arc  would  be  converted  into  light  energy.  This  object  is 
partially  realized  in  the  so-called  flaming  arcs.  In  these,  the 
positive  carbon  is  either  impregnated  with  certain  salts  of  cal- 
cium or  of  magnesium  or  has  a  core  filled  with  these  salts.  The 
vapor  produced  when  these  salts  are  volatilized  is  highly  heated 
and  emits  a  powerful  reddish  yellow  light,  and  since  it  con- 
ducts it  also  permits  the  carbons  to  be  separated  by  upwards 
of  an  inch.  They  need  not  be  raised  to  such  a  high  temperature 
as  in  the  common  arc  lamps  and  therefore  their  life  is  longer. 
The  efficiency  of  these  lamps  is  at  least  three  times  that  of  the 
common  form. 

Instead  of  the  carbons  being  in  the  same  vertical  line,  they  are 
sometimes  arranged  both  pointing  downward  like  the  letter  V, 
the  arc  being  at  the  vertex.  In  this  way,  neither  carbon  screens 
the  other  and  both  tips  throw  their  light  down.  There  is  a  tend- 
ency, however,  for  the  arc  to  ascend  between  the  carbons.  This 
is  corrected  by  arranging  a  magnetic  field,  similar  to  the  magnetic 
blow-out  (Par.  485),  but  only  strong  enough  to  keep  the  arc  down 
at  the  tips  of  the  carbons. 

An  additional  advantage  of  this  arrangement  is  that  the  slag 
formed  by  the  fusion  of  the  impregnating  salts  drops  off  and  does 
not  clog  the  tips  of  the  carbons  with  a  non-conducting  glassy 
material. 


412  ELEMENTS  OF  ELECTRICITY. 

523.  The  Magnetite  Arc  Lamp. — The  magnetite  arc  lamp,  but 
recently  developed  and  used  with  direct  current  only,  resembles 
the  flaming  arc  lamp  in  that  the  chief  source  of  light  is  the  arc 
which  is  an  inch  or  more  in  length.    It  differs  from  other  arc  lamps 
in  that  little  or  no  light  is  given  off  by  the  electrodes,  also  that  the 
maximum  amount  of  light  is  developed  at  the  negative  end  of  the 
arc.    The  positive  electrode  is  of  copper  and  is  of  such  size  that 
the  heat  developed  is  conducted  away  so  that  the  electrode  is  not 
consumed.    The  negative  electrode  is  a  thin  steel  tube,  the  size 
and  shape  of  an  ordinary  carbon.    It  is  packed  with  a  mixture  of 
powdered  magnetite,  Fe304,  and  oxides  of  chromium  and  titanium. 
The  magnetic  oxide  renders  the  electrode  a  conductor,  the  remain- 
ing oxides  not  conducting  until  they  have  been  heated.    The  oxide 
of  titanium  imparts  the  luminosity  to  the  arc;  the  oxide  of  chro- 
mium increases  the  life  of  the  electrode.    An  eight-inch  electrode 
in  such  a  lamp  with  a  current  of  4  amperes  at  a  pressure  of  80  volts 
will  burn  for  upwards  of  200  hours.    Since  the  constituents  of  the 
electrode  are  oxides,  there  is  no  combustion  and  the  arc  is  not 
enclosed.     These  oxides,  however,  are  volatilized  and  condense 
immediately  beyond  the  limits  of  the  arc  in  a  reddish  soot  which 
if  not  removed  soon  covers  globes,  reflectors,  etc.    It  is  therefore 
necessary  in  these  lamps  to  provide  some  form  of  chimney  with  a 
strong  draught  by  which  this  deposit  is  carried  off. 

524.  Efficiency  of  Arc  Lights. — The  efficiency  of  an  arc  light  is 
much  greater  than  that  of  an  incandescent  lamp.    The  common 
arc  lamp,  carrying  a  current  of  about  10  amperes  at  a  pressure  of 
about  50  volts,  develops  2000  candle-power  in  the  zone  of  maxi- 
mum luminosity,  or,  in  round  numbers,  one  candle-power  per  0.25 
watt.    The  mean  spherical  candle-power  (Par.  509)  is,  however, 
considerably  less  than  2000.    The  larger  search  lights,  taking  200 
amperes  at  60  volts,  develop  nearly  eight  candle-power  per  watt, 
but  it  must  be  noted  that  there  is  a  lack  of  agreement  and  much 
uncertainty  as  to  the  measurement  of  the  candle-power  of  these 
powerful  lights. 

525.  Luminous  Vapor  Lamps.— Suppose  a  high  voltage,  such  as 
that  produced  by  an  induction  coil,  be  applied  to  two  platinum 
wires  sealed  into  the  opposite  ends  of  a  glass  tube,  and  suppose 
that  at  the  same  time  an  air  pump  be  set  to  work  to  exhaust  the 
air  from  the  tube.    If  the  wires  be  not  too  far  apart,  sparks  will 


ELECTRO-MAGNETICS.  413 

pass  between  them,  but  as  the  air  is  exhausted,  these  sparks  lose 
their  definiteness  and  finally  take  the  form  of  an  effulgence  or  glow 
completely  filling  the  tube.  The  color  of  this  glow  varies  with  the 
nature  of  the  gas  enclosed  in  the  tube.  For  air,  it  is  rosy  pink;  for 
nitrogen,  yellow;  for  carbon  dioxide,  white.  At  this  stage  the  rare- 
fied gas  has  great  conductivity.  If  the  exhaustion  of  the  tube  be 
continued,  the  conductivity  decreases,  the  luminous  column  begins 
to  break  up  in  striae  and  finally  disappears.  When  the  pressure 
has  been  reduced  to  about  one-millionth  of  an  atmosphere,  the 
glass  itself  begins  to  phosphoresce.  Beyond  this,  the  resistance 
becomes  so  great  that  no  current  can  be  sent  through  the  tube. 
There  is  therefore  a  stage  of  rarefaction  in  which  gases  conduct 
electricity  and  in  doing  so  emit  light,  and  these  effects  diminish 
if  the  pressure  be  increased  or  decreased  from  what  it  is  at  this 
stage.  Explanation  of  this  will  be  given  later;  for  the  time  being 
it  will  suffice  to  say  that  when  highly  rarefied  these  gases  ionize 
and  therefore  conduct  (Par.  276).  If  the  exhaustion  be  complete, 
there  are  no  ions  left  and  consequently  a  vacuum  is  a  non-con- 
ductor. 

The  foregoing  is  the  principle  of  the  luminous  vapor  lamps,  two 
of  which  we  shall  now  describe.  Their  luminous  efficiency  is  very 
high,  for  while  in  the  ordinary  carbon  filament  lamp  less  than  one 
per  cent  of  the  total  energy  expended  is  developed  as  light,  in 
these  luminous  vapor  lamps  twenty  per  cent  or  more  is  so  develop- 
ed. They  have  not  yet  been  made  in  small  units  but  are  rather 
used  for  general  illumination  of  large  spaces. 


Fig.  251. 

526.  The  Moore  Light.— The  apparatus  for  producing  this 
light,  shown  diagrammatically  in  Fig.  251,  takes  the  form  of  an 
exhausted  glass  tube  one  and  three-quarters  inches  in  diameter  and 
of  any  length  up  to  200  feet.  It  is  usually  suspended  along  the 


414  ELEMENTS  OF  ELECTRICITY. 

ceiling  of  the  room  to  be  illuminated.  When  in  operation,  it  emits 
a  soft,  diffused  light,  without  flickering  or  unsteadiness,  the  color 
varying,  as  stated  in  the  preceding  paragraph,  according  to  the 
gas  contained  in  the  tube.  To  produce  a  light  of  fifteen  candle- 
power  per  running  foot,  about  70  volts  per  foot  are  required,  the 
corresponding  current  being  about  one-third  of  an  ampere.  By 
increasing  the  voltage,  the  candle-power  can  be  raised  to  a  maxi- 
mum of  thirty  per  foot.  A  tube  100  feet  long  requires  7150  volts. 
This  high  voltage  is  obtained  from  an  alternating  current  by  means 
of  a  simple  step  up  transformer,  as  shown  in  the  figure  above. 

As  the  lamp  is  used,  the  gas  in  the  tube  appears  to  be  consumed 
and  the  rarefaction  increases.  This  causes  the  resistance  to  in- 
crease. It  therefore  becomes  necessary  to  introduce  from  time  to 
time  minute  amounts  of  gas,  and  a  simple  and  effective  automatic 
valve  has  been  devised  for  this  purpose. 

527.  The  Cooper  Hewitt  Mercury  Vapor  Lamp. — If  in  a  glass 
tube,  otherwise  vacuous,  there  be  introduced  a  small  amount  of 
mercury,  the  vacuous  space  would  quickly  become  filled  with  the 
vapor  of  mercury  (Par.  277).  An  electric  current  passed  through 
this  vapor  would  cause  it  to  glow  with  a  greenish  light.  This 
arrangement  would  not  differ  in  principle  from  the  Moore  light, 
just  described.  In  investigating  it,  however,  Cooper  Hewitt  dis- 
covered some  remarkable  properties.  Thus,  at  the  outset,  its 
resistance  is  so  great  as  to  require  several  thousand  volts  to  start 
the  current  through  it.  This  resistance  seems  to  be  confined  to 
the  surface  of  the  negative  electrode,  and  is  temporarily  destroyed 
by  the  passage  of  a  current.  Although  several  thousand  volts 
are  required  to  start  the  current  through  a  tube  twenty  inches 
long,  when  once  started  it  may  be  maintained  by  a  pressure  of 
50  volts,  provided  it  does  not  fall  below  one  ampere.  If  it  falls 
below  this,  the  negative-electrode  resistance  re-asserts  itself,  the 
current  ceases,  and  the  high  voltage  is  required  to  start  the  cur- 
rent again. 

Various  forms  of  this  lamp  have  been  devised,  all  alike  in  princi- 
ple but  differing  in  the  arrangements  for  starting.  A  common 
form  is  shown  in  Fig.  252.  This  particular  lamp,  designed  for  use 
in  a  100  volt  circuit,  and  taking  a  current  of  three  and  a  half 
amperes,  consists  of  a  one-inch  glass  tube,  AB,  45  inches  long  and 
shaped  as  shown.  It  is  supported  by  a  frame  CD,  which  carries 
the  lead  wires  and  which  hangs  from  the  suspension  bar  E.  The 


ELECTRO-MAGNETICS.  415 

canopy  F  contains  the  various  coils  and  electro-magnets  used  in 
connection  with  the  lamp.  The  tube  is  exhausted  to  a  pressure  of 
one  millimeter.  The  positive  electrode  A  is  df  iron,  a  metal  to 
which  mercury  does  not  adhere,  and  the  negative  electrode  B  is  a 
small  puddle  of  mercury. 


Fig.  252. 


To  start  the  lamp,  the  ring  attached  to  A  is  pulled  down,  the 
lamp  and  frame  rotating  about  the  point  E  until  A  is  slightly 
below  the  level  of  B.  The  mercury  in  B  flows  down  the  tube 
and  makes  contact  at  A.  This  little  stream  of  mercury  between 
A  and  B  would  act  as  a  short  circuit  were  it  not  for  a  ballasting 
coil  (Par.  508)  in  the  canopy  F.  The  ring  is  now  released,  the 
lamp  tips  back  to  its  original  position  and  the  mercury  runs  back 
into  B.  In  doing  so,  the  thread  of  mercury  breaks  at  some  point 
producing  a  flash-like  arc,  volatilizing  some  of  the  metal  and 
ionizing  the  vapor  so  that  the  lamp  starts.  This  voltage  at  break 
is  aided  by  an  inductance  coil  in  series.  In  the  smaller  sizes  of 
lamps,  this  tipping  is  done  by  electro-magnets.  Several  other 
starting  devices  are  in  use. 

This  form  of  lamp  can  be  used  with  direct  current  only,  but 
others  are  made  for  use  with  alternating  currents.  The  principle 
of  these  latter  will  be  explained  when  the  subject  of  the  mercury 
arc  rectifier  is  reached. 

The  efficiency  of  the  light  is  high,  being  0.64  watt  per  candle- 
power.  It  is  rich  in  actinic  rays  and  especially  valuable  for  photog- 
raphy, blue  printing,  etc.,  but  has  one  very  grave  objection.  It 
is  devoid  of  red  rays  and  red  objects  placed  in  it  appear  purple  or 
black.  It  imparts  to  persons  a  peculiarly  ghastly  appearance  and 
can  not  be  used  where  colors  are  to  be  shown  in  their  proper  rela- 
tion. No  way  has  yet  been  discovered  of  adding  the  needed  red. 


416 


ELEMENTS  OF  ELECTRICITY. 


CHAPTER  38. 
THERMO-ELECTRICS. 

528.  Seebeck's  Discoveries. — In  1821,  in  investigating  Volta's 
contact  series  (Par.  187),  Seebeck  discovered  that  in  a  circuit  com- 
posed of  two  metals,  if  one  of  the  junctions  be  at  a  different  tem- 
perature from  the  other,  an  E.  M.  F.  and  current  will  be  produced. 
Fig.  253  represents  a  circuit  composed  of  a  strip  of  copper  and  one 


B 


Fig.  253. 


of  iron  which  are  joined  at  the  points  A  and  B.  The  strips  may  be 
welded,  or  soldered,  or  simply  pressed  together.  If  the  junction 
A  be  heated  so  that  its  temperature  is  higher  than  that  of  B,  a 
current  will  flow  around  the  circuit  in  the  direction  indicated  by 
the  arrows,  that  is,  at  the  cool  junction  it  will  flow  from  the  iron 
to  the  copper,  and  at  the  hot  junction,  from  the  copper  to  the  iron. 
The  needle  placed  within  the  circuit  will  indicate  this  current. 
The  two  metals  constitute  a  thermo-couple,  and  the  E.  M.  F.  pro- 
duced is  called  the  thermo-electric  electro-motive  force.  Seebeck 
found  further  that  this  E.  M.  F.  varied  (a)  with  the  metals  used 
and  (b)  with  the  difference  of  temperature  of  the  junctions,  and  he 
was  able  to  arrange  the  following  thermo-electric  series  in  which,  in 
a  thermo-couple  composed  of  any  two,  the  current  at  the  cold 
junction  flows  from  the  metal  higher  on  the  list  to  the  metal  which 
is  lower. 


ELECTRO-MAGNETICS. 


417 


Thermo- Electric  Series. 
Antimony  Tin 

Iron  Lead 

Zinc  Copper 

Silver  Platinum 

Gold  Bismuth 

In  accordance  with  these  observations,  thermo-couples  are 
usually  made  of  antimony  and  bismuth,  though  certain  metallic 
sulphides  may  also  be  used.  The  E.  M.  F.  produced  is  very  feeble. 
Even  for  an  antimony-bismuth  couple,  it  is  only  about  one  ten- 
thousandth  of  a  volt  per  degree  Centigrade,  or  if  one  junction  of 
such  a  couple  be  placed  in  boiling  water,  the  other  in  melting  ice, 
the  E.  M.  F.  will  be  about  one-hundredth  of  a  volt. 

529.  Thermo-Electric  Inversion. — In  1823  Gumming  added  to 
the  discoveries  of  Seebeck  by  showing  that  the  thermo-electric 


0 


V 


\ 


Fig.  254. 


E.  M.  F.  varied  not  only  with  the  difference  of  temperature  of  the 
two  junctions  but  also  with  their  actual  temperatures,  Thus,  if 
one  junction  of  the  copper-iron  couple  shown  in  Fig.  253  be  kept 
at  a  constant  temperature  and  the  other  be  heated  so  that  its  tem- 
perature increases  at  a  uniform  rate,  the  E.  M.  F.  will  at  first  also 
increase  uniformly  but  finally  will  slacken  and  will  reach  a  maxi- 
mum at  275°  C,  after  which  it  will  decrease.  This  is  shown 
graphically  by  the  curve  in  Fig.  254,  in  which  the  abscissae  repre- 
sent temperatures  and  the  ordinates  the  corresponding  E.  M.  F. 
The  temperature  Ot,  at  which  the  E.  M.  F.  te  is  a  maximum,  is 
called  the  neutral  temperature  and  varies  for  each  different  pair  of 


418  ELEMENTS  OF  ELECTRICITY. 

metals.  If  the  temperature  of  the  junctions  be  equally  distant 
from  t,  the  E.  M.  F.  is  zero.  Thus  at  OT  =2  xOt,  the  E.  M.  F.  is 
zero  and  beyond  T  it  is  negative,  hence  the  current  is  reversed  and 
OT  is  called  the  temperature  of  inversion.  Had  the  constant 
temperature  of  one  junction  been  Of  instead  of  0,  the  maximum 
E.  M.  F.  would  have  been  me,  the  neutral  temperature  remaining 
unchanged.  This  thermo-electric  curve  has  been  shown  by  Lord 
Kelvin  to  be  a  parabola. 

530.  The  Peltier  Effect. — From  what  has  just  been  seen,  if  one 
junction  of  an  antimony-bismuth  thermo-couple  be  heated,  as 

B 


w////y//////^^^ 


ANTIMONY  BI5MUTH 


Fig.  255. 

shown  in  Fig.  255,  a  current  will  flow  around  the  circuit  as  indi- 
cated by  the  arrows,  that  is,  flowing  at  the  cold  junction  B  from 
the  antimony  to  the  bismuth. 

If  the  source  of  heat  be  now  removed,  the  current  will  still  con- 
tinue to  flow  so  long  as  the  junction  A  is  at  a  higher  temperature 
than  the  junction  B.  The  only  conceivable  source  of  this  current 
is  the  heat  energy  at  A,  and  since  this  heat  energy  is  converted 
into  electrical  energy,  there  must  be  at  that  point  an  absorption 
and  disappearance  of  heat.  Also,  since  the  actual  current  through 
the  junction  B  is  opposite  in  direction  to  the  current  which  would 
have  been  produced  by  the  absorption  of  heat  at  that  point, 
the  logical  inference  is  that  heat  is  developed  at  B.  The  correct- 
ness of  this  inference  was  shown  by  Peltier  in  1834.  A  bar  of  anti- 
mony and  one  of  bismuth  were  placed  crosswise  as  shown  in  Fig. 
256  and  were  soldered  together.  Between  the  ends  C  and  B  were 
connected  a  galvanometer  G  and  a  key  S.  Between  A  and  D  were 
connected  a  battery  and  a  key  K.  K  was  closed  for  a  while, 
allowing  a  current  to  flow  around  the  triangular  circuit  in  the 
direction  DEA,  or  passing  at  the  junction  from  the  bismuth  to 


ELECTRO-MAGNETICS.  419 

the  antimony.  K  was  then  opened  and  S  was  closed.  The  gal- 
vanometer immediately  indicated  a  current  from  C  to  B,  showing 
that  the  junction  E  had  been  cooled  below  the  temperature  of  B 
and  C  by  the  passage  of  the  current  from  the  battery.  The  battery 
was  now  reversed  so  that  when  K  was  closed  the  current  flowed  in 
the  direction  AED,  or  from  the  antimony  to  the  bismuth.  After 
a  while,  K  was  again  opened  and  S  closed.  The  galvanometer  now 
indicated  a  current  from  B  to  C,  showing  that  the  junction  E  had 
been  heated  above  the  temperature  of  B  and  C. 


Fig.  256. 

We  thus  see  that  when  a  current  is  passed  across  the  junction 
of  two  dissimilar  metals,  heat  is  evolved  if  the  current  flows  from 
the  metal  that  is  the  higher  in  the  thermo-electric  series  (Par.  528), 
and  heat  is  absorbed  if  it  flows  from  the  metal  that  is  the  lower 
in  this  series. 

This  heating  or  cooling  produced  by  the  passage  of  a  current 
across  the  junction  of  two  dissimilar  metals  is  called  the  Peltier 
effect,  and  is  entirely  distinct  from  the  Joule  effect  discussed  in 
Chapter  35.  The  Joule  effect  varies  as  the  square  of  the  current 
and  is  independent  of  the  direction  of  flow;  the  Peltier  effect  varies 
as  the  first  power  of  the  current  and  is  reversed  if  the  direction  of 
the  flow  be  reversed. 

In  the  manufacture  of  very  delicate  electrical  measuring  instru- 
ments, consideration  must  be  given  to  these  various  thermo-elec- 
tric effects.  If  in  the  circuit  of  such  instruments  a  junction  of 
different  metals  occurs,  the  heating  effect  of  the  current  may  set 
up  thermo-electric  effects  which  might  cause  appreciable  error  in 
the  indications  of  the  instrument. 


420  ELEMENTS  OF  ELECTRICITY. 

531.  The    Thomson    Effect. — Sir    William    Thomson    (Lord 
Kelvin)  showed  that  when  a  current  flows  through  a  homogeneous 
conductor  which  is  heated  at  one  point  more  than  at  another,  heat 
is  either  developed  or  absorbed,  depending  upon  the  nature  of  the 
conductor  and  the  direction  of  the  current.    Thus,  in  a  copper  wire 
whose  center  is  hotter  than  the  ends,  heat  is  absorbed  by  the  cur- 
rent as  it  flows  towards  the  hot  center  and  evolved  as  it  flows  from 
this  center.    With  an  iron  wire,  these  effects  are  reversed,  heat 
being  developed  in  the  first  half  and  absorbed  in  the  second.    This 
Thomson  effect  has  not  been  observed  in  lead  and  consequently  lead 
is  taken  as  the  standard,  or  is  made  one  of  the  elements  in  each 
thermo-couple  which  is  tested  in  order  to  determine  the  thermo- 
electric power  of  the  various  metals. 

The  subject  of  thermo-electricity  is  susceptible  of  elaborate 
mathematical  treatment  but  its  importance  is  not  now  sufficient 
to  warrant  a  more  extended  discussion.  We  shall  therefore  pass 
at  once  to  a  description  of  some  of  its  practical  applications. 

532.  The  Thermopile.— Although,  as  stated  above  (Par.  528), 
the  E.  M.  F.  of  a  thermo-couple  is  very  feeble,  if  a  number  of  these 
couples  arranged  in  the  same  order  be  connected  in  series  and  the 
alternate  junctions  be  heated,  the  E.  M.  F.s  will  all  act  in  the  same 
direction  and  the  total  E.  M.  F.  will  be  the  sum  of  the  separate 
E.  M.  F.s,  in  other  words,  the  arrangement  is  similar  to  a  battery 

composed  of  a  number  of  cells  con- 
nected in  series.  Such  an  arrange- 
ment is  called  a  thermopile. 

Many  forms  of  thermopiles  have 
been  devised.  For  example,  the 
couples  may  be  grouped  as  shown 
in  Fig.  257  like  the  spokes  of  a 
wheel  radiating  from  a  central  cy- 
lindrical opening,  and  there  may 
be  a  number  of  these  groups 
placed  one  above  the  other  and  all 
connected  in  series.  The  interior 
Fi  257  cylinder  may  then  be  heated  by  a 

small  furnace,  by  gas  jets,  or  by 

hot  water,  the  outer  ends  of  the  couples  being  cooled  by  the  air. 
At  first  sight  it  seems  that  the  thermopile  affords  a  satisfactory 

solution  of  an  extremely  important  problem,  the  direct  conversion 


ELECTRO-MAGNETICS. 


421 


of  heat  energy  into  electrical  energy  without  the  usual  interme- 
diate steps  of  heating  water,  producing  steam,  utilizing  the  expan- 
sion of  the  steam  to  produce  rotation,  and  by  means  of  this  rota- 
tion producing  electricity  as  outlined  in  Par.  423,  each  of  which 
steps  is  accompanied  by  inevitable  loss  of  energy.  Thermopiles 
have  been  constructed  to  furnish  the  small  currents  required  in 
gold  and  silver  plating,  and  are  used  in  certain  extremely  sensitive 
heat-measuring  instruments  (Par.  533),  but  where  electricity  is  to 
be  supplied  on  a  large  scale,  they  are  a  failure.  The  Joule  effect, 
the  Peltier  effect  and  the  heat  conductivity  of  the  two  metals  all 
tend  to  raise  the  temperature  of  the  cool  junctions  and  thus 
decrease  the  E.  M.  F.,  and  the  couples  themselves  deteriorate 
rapidly  with  use.  Their  efficiency  is  very  low,  less  than  one-half 
of  one  per  cent  of  the  heat  energy  being  converted  into  electrical 
energy. 

533.  The  Radiometer. — There  has  been  employed  for  the  com- 
parison of  radiant  heat  from  different  sources,  a  thermopile  con- 
sisting of  a  rectangular  bundle  of  thermo-couples  arranged  in  series 
and  mounted  in  a  frame  as  shown  in  Fig.  258.  The  contiguous 


Fig.  258. 

couples  and  the  metal  strips  of  each  couple,  except  at  the  junctions, 
are  insulated  from  each  other  by  sheets  of  mica.  The  first  and 
last  strips  of  the  series  are  connected  to  terminals  T,  which  are 
attached  one  on  each  side  of  the  frame.  The  pile,  except  the  end 
which  is  to  receive  the  radiant  heat,  is  shielded  by  a  protecting 
hood.  The  receiving  end  is  coated  with  lampblack,  the  best 
absorbent  of  heat.  When  in  use,  a  sensitive  galvanometer  is  con- 
nected to  the  terminals,  the  current  through  the  galvanometer 
varying  directly  as  the  difference  of  temperature  of  the  hot  and 
cold  faces  of  the  pile. 


422 


ELEMENTS  OF  ELECTRICITY. 


Thermometers  and  pyrometers  have  been  constructed  on  the 
principle  of  the  thermopile.  In  the  pyrometers,  the  couple  is  com- 
posed of  platinum  and  rhodium. 

534.  The  Radio- Micrometer. — An  extremely  sensitive  form  of 
radiometer,  the  radio-micrometer,  has  been  devised  by  Vernon 
Boys.  It  combines  the  principles  of  the  thermo-couple  and  the 
d'Arsonval  galvanometer.  As  shown  diagram- 
matically  in  Fig.  259  it  differs  from  the  d'Arsonval 
galvanometer  (Par.  378)  only  in  that  a  quartz 
fibre  is  substituted  for  the  phosphor-bronze  sus- 
pension, and  the  coil  consists  of  a  single  vertically- 
elongated  loop  of  copper  wire.  To  the  lower  ends 
of  this  loop  there  are  soldered  two  small  bars  of 
antimony  and  bismuth  and  these  bars  are  con- 
nected by  a  little  sheet  of  lampblack-coated  copper 
foil,  only  one-tenth  of  an  inch  square.  When 
the  copper  foil  is  heated,  the  E.  M.  F.  of  the 
couple  is  very  small  but,  since  the  resistance  of 
the  copper  loop  is  also  small,  the  current  is  ap- 
preciable and  the  loop  moves  in  accordance  with 
Maxwell's  law  (Par.  371),  the  deflection  being  observed  by  means 
of  the  mirror  M.  It  is  said  that  a  change  in  the  temperature  of 
the  copper  foil  of  one-millionth  of  a  degree  will  cause  a  deflection 
of  one  division  on  the  scale,  and  that  the  radiant  heat  of  a  candle 
can  be  detected  at  a  distance  of  two  miles.  Instruments  of  this 
kind,  known  also  as  bolometers,  have  been  used  to  measure  the 
heat  radiated  from  the  stars  and  to  compare  the  heat  emitted 
from  different  portions  of  the  solar  spectrum. 


Fig.  259. 


ELECTRO-MAGNETICS.  423 


CHAPTER  39. 

REMARKS   ON   CERTAIN   ELECTRIC   UNITS. 

535.  Two  Systems  of  Electric  Units. — There  are  two  distinct 
systems  of  electric  units;  one,  the  electro-static,  based  upon  the 
interaction  of  static  charges;  the  other,  the  electro-magnetic,  based 
upon  the  interaction  of  a  magnetic  pole  and  the  field  produced 
about  a  conductor  carrying  a  current.    The  electro-magnetic  units, 
and  the  derived  practical  units,  are,  on  account  of  their  suitability 
for  practical  purposes,  used  to  the  exclusion  of  those  of  the  electro- 
static system.    Nevertheless,  it  is  desirable  for  the  student  to  be 
acquainted  with  both  systems  and  to  understand  the  relation  ex- 
isting between  them. 

In  the  electro-static  system,  the  starting  point  is  the  unit  quan- 
tity, which  is  defined  (Par.  56)  as  that  quantity  which  when  placed 
at  a  distance  of  one  centimeter  in  air  from  a  similar  and  equal 
quantity,  repels  it  with  a  force  of  one  dyne. 

In  the  electro-magnetic  system,  the  starting  point  is  the  unit 
pole,  or  (Par.  133)  that  pole  which,  when  placed  at  a  distance  of  one 
centimeter  from  a  similar  and  equal  pole,  repels  it  with  a  force  of 
one  dyne. 

536.  Units  of  Current  and  Quantity. — Thus  far,  there  does  not 
seem  to  be  much  to  choose  between  the  two  systems.    In  the  next 
step,  however,  there  is  a  marked  difference. 

In  the  electro-static  system  the  unit  current  is  that  current 
which  conveys  unit  quantity  in  unit  time. 

In  the  electro-magnetic  system,  the  unit  current  can  not  be 
defined  so  simply.  We  have  shown,  however  (Par.  353),  that  a 
current  flowing  in  a  conductor  establishes  about  that  conductor 
a  magnetic  field  which  varies  directly  with  the  current.  There- 
fore, with  other  conditions  constant,  we  may  take  the  strength  of 
the  field  produced  as  a  measure  of  the  strength  of  the  current,  and 
the  simplest  way  to  compare  magnetic  fields  is  to  compare  the 
forces  which  they  exert  upon  the  same  pole.  The  electro-magnetic 
unit  of  current  is  therefore  defined  (Par.  355)  as  that  current  which, 


424  ELEMENTS  OF  ELECTRICITY. 

flowing  through  one  centimeter  of  a  conductor  bent  into  the  arc  of 
a  circle  whose  radius  is  one  centimeter,  exerts  a  force  of  one  dyne 
upon  a  unit  pole  placed  at  the  center  of  the  circle.  This  current, 
we  have  seen,  is  ten  amperes. 

Having  thus  defined  the  unit  current,  we  may  now  define  the 
electro-magnetic  unit  of  quantity  as  that  quantity  conveyed  by 
unit  current  in  unit  time.  The  ampere  flowing  for  one  second 
conveys  one  coulomb;  the  absolute  unit  of  quantity  is  therefore 
equal  to  ten  coulombs.  It  is  thus  seen  that  in  the  electro-static 
system  we  pass  from  unit  quantity  to  unit  current;  on  the  other 
hand,  in  the  electro-magnetic  system,  we  pass  from  unit  current 
to  unit  quantity. 

By  experiments  and  measurements  based  on  widely  different 
methods,  it  has  been  found  that  the  electro-magnetic  unit  of 
quantity  is  about  (2.98+)(1010)  times  as  great  as  the  electro- 
static unit  of  quantity.  For  round  numbers,  this  is  taken  as 
3X1010,  or  thirty  billion.  The  coulomb,  therefore,  as  has  already 
been  stated  (Par.  56),  is  three  billion  (3X109)  times  as  great  as 
the  electro-static  unit. 

537.  Units  of  Electro -Motive  Force. — In  either  system,  unit 
difference  of  potential  exists  between  two  points  when  the  expendi- 
ture of  one  erg  is  required  to  convey  a  unit  of  quantity  of  elec- 
tricity from  one  to  the  other.    The  electro-magnetic  unit  of  poten- 
tial is  therefore  ~ TTT^  times  the  electro-static  unit  of  potential. 

o  /\  J.U 

In  Par.  427  it  was  stated  that  108  absolute  electro-magnetic  units 
of  potential  were  equal  to  one  volt.  The  volt  is  therefore  3  X  1010~8 
=  3  XlO2  =  300  times  as  small  as  the  electro-static  unit  of  potential, 
or,  as  was  stated  in  Pars.  77  and  78,  the  electro-static  difference  of 
potential  in  ergs  must  be  multiplied  by  300  to  reduce  it  to  volts. 

538.  Primary  Electro-Magnetic  Units.— The  units  of  E.  M.  F., 
current  and  resistance  are  bound  together  by  Ohm's  law,  I  =  E/R, 
which  necessarily  is  true  whatever  units  be  employed,  that  is, 
whether  we  use  the  absolute  or  the  practical  units.    It  follows  that 

absolute  unit  of  E.  M.  F. 


absolute  unit  of  current 


absolute  unit  of  resistance 


If,  therefore,  any  two  of  these  units  be  fixed  upon,  the  third  follows 
as  a  matter  of  course;  or,  it  suffices  to  define  any  two,  and  these 


ELECTRO-MAGNETICS.  425 

definitions  fix  the  third.  It  was  this  consideration  that  led  to  the 
definition  of  resistance  as  a  ratio,  to  which  definition  attention  was 
called  in  Par.  307. 

The  question  now  arises,  which  two  shall  be  selected  as  our 
primary  units. 

In  Par.  355,  the  definition  of  the  absolute  unit  of  current  was 
given  (repeated  in  the  preceding  paragraph),  and  in  Par.  374  it  was 
shown  how  by  means  of  the  tangent  galvanometer  a  current  could 
be  measured  in  absolute  units.  The  absolute  unit  of  current  is 
therefore  selected  as  one  of  the  primary  units. 

Reflection  will  show  that  of  the  three  units,  resistance  is  the  only 
one  which  could  be  perpetuated  in  a  material  standard,  such  as  a 
given  length  of  a  certain-sized  wire  of  a  specified  material.  If 
resistance  could  be  measured  absolutely,  it  would  naturally  be 
selected  as  the  second  primary  unit.  We  shall  now  explain  how 
this  may  be  done,  but  preliminary  thereto  we  must  develop  an- 
other conception  of  electric  resistance. 

539.  Dimensional  Formulae.  —  It  has  been  shown  (Par.  10)  that 
the  fundamental  units  of  our  system  are  the  centimeter,  the  gram 
and  the  second,  and  that  all  the  other  units  are  derived  from  these. 
It  is  therefore  possible  to  express  any  derived  unit  in  terms  of 
length,  mass  and  time.    Such  expressions  are  called  the  dimensional 
formulae  of  the  units  in  question.    A  study]  of  these  dimensional 
formulae  will  afford  a  clearer  conception  of  the  nature  of  the  units 
and  will  bring  to  light  unexpected  relations. 

540.  Dimensional  Formulae  of  Electro-Magnetic  Resistance.  — 

From  Ohm's  law,  R  =  E/I.  E,  the  difference  of  potential,  is  meas- 
ured by  the  work  done  in  moving  unit  quantity  of  electricity 
through  a  difference  of  potential  E.  If  to  move  Q  units  the  work 
done  is  W,  then  to  move  one  unit,  the  work  is  W/Q,  whence 

W 

*  CD 


But  work  =  forceXpath=FxL,  and  Q  =  IxT.     Substituting 

these  values  in  (I)  p  v  r 

E  =      x 
IX  T 

Substituting  this  for  E  in  Ohm's  law 

«  =     x  (II) 


426 


ELEMENTS  OF  ELECTRICITY. 


Two  poles,  each  of  strength  m,  at  a  distance  L  apart  exert  upon 
each  other  a  force  F=m?/L2,  whence 

m  =  V*\Z?  (Ill) 

A  pole  of  strength  m  placed  in  a  magnetic  field  of  strength  H  is 
acted  upon  by  a  force  F=m.H,  whence  H=F/m.  \ 

The  field  produced  at  the  center  of  a  circular  coil  by  a  current 
/  (Par.  354)  is  proportional  to  I/L,  orH  =  I/L,  L  being  the  radius 
of  the  coil.  Equating  these  two  values  of  H  and  solving  for  m,  we 
have  m=F.L/I. 

Substituting  this  value  of  m  in  (III),  and  solving,  we  have 
F  =  72,  whence  (II)  becomes 

R  =  L/T 

But  L  is  length  and  T  is  time,  hence  resistance  is  of  the  nature 
of  a  velocity. 

541.  Resistance  Expressed  as  Velocity. — Why  it  is  possible  to 
express  resistance  as  a  velocity  may  be  shown  as  follows:  Let  Fig. 


AMMETER 


Fig.  260. 

260  represent  the  arrangement  of  parallel  rails  and  sliding  cross 
bar  which  we  have  already  described  several  times.  Suppose  the 
rails  to  be  of  negligible  resistance,  to  be  one  centimeter  apart  and 
to  embrace  between  them  a  uniform  unit  field.  AB,  moving  with 
uniform  velocity,  is  slid  along  towards  D,  which  is  at  an  indefinite 
distance  to  the  left.  If  AB  moves  V  centimeters  per  second  it  will 
cut  V  lines  of  force  and  will  generate  V  absolute  units  of  E.  M.  F., 
in  direction  from  A  to  B  (Par.  422).  If  the  resistance  of  A  B  be  Rt 
the  current  through  AB  will  be 

I  =  v 

Since  the  current  varies  directly  with  V,  the  velocity  of  AB,  it 
is  possible  to  move  AB  rapidly  enough  to  make  7  one  absolute 
unit  of  current.  When  7  becomes  1,  the  above  expression  becomes 
R  =  V,  or  R  is  expressed  as  a  velocity. 


ELECTRO-MAGNETICS.  427 

If  R  be  one  ohm,  in  order  to  drive  a  current  of  one  absolute  unit 
through  AB,  it  must  be  moved  with  a  velocity  of  109  centimeters 
(ten  million  meters,  or  one  earth's  quadrant  per  second  (Par.  4) ). 

From  the  foregoing,  knowing  the  strength  of  the  field  between 
the  rails  and  the  velocity  with  which  AB  is  moved,  we  could  deter- 
mine V.  The  current  in  the  circuit  could  be  read  from  an  ammeter 
at  Z).  Thus  having  V  and  7,  the  quotient  of  the  former  by  the 
latter  would  give  R,  the  resistance  of  AB.  Practically,  such  a 
determination  is  impossible.  A  B  could  not  be  moved  for  a  suffi- 
cient length  of  time  with  the  desired  rapidity;  it  would  not,  as  it 
moved,  maintain  unvarying  contact  with  the  rails;  and  finally, 
the  resistance  of  the  rails  is  not  negligible,  hence  the  resistance  of 
the  circuit  would  continually  decrease.  However,  several  methods 
have  been  devised  by  which  these  difficulties  are  obviated  and  we 
shall  now  explain  one,  first  proposed  by  Weber  and  improved  by 
later  investigators. 

542.  Absolute  Measurement  of  Resistance. — In  Fig.  261,  AB 
represents  a  circular  coil  of  a  number  of  turns  of  wire,  the  ends  of 


Fig.  261. 

the  coil  being  joined  together.  It  is  mounted  upon  a  vertical  axis 
about  which  it  may  be  spun  rapidly.  Through  an  opening  in  the 
top  there  extends  a  silk  fibre  from  which  there  hangs  at  the  center 
of  the  coil  a  needle.  The  arrows  H  represent  lines  of  force  of  the 
earth's  field.  If  the  coil,  viewed  from  above,  be  spun  in  a  clock- 
wise direction,  it  will  cut  the  lines  H  and  consequently  an  E.  M.  F. 
will  be  induced.  Application  of  the  right  hand  rule  (Par.  422)  will 
show  that  as  the  side  B  moves  from  B  to  A,  it  will  generate  an 
E.  M.  F.  acting  upward  and  during  the  same  time  a  downward 


428  ELEMENTS  OF  ELECTRICITY. 

E.  M.  F.  will  be  generated  in  the  side  A,  that  is,  there  will  be  in- 
duced in  the  coil  a  current,  which,  viewed  from  the  point  P  (a 
point  on  the  horizontal  axis  of  the  coil  perpendicular  to  the  meri- 
dian), will  be  counter-clockwise  in  direction.    As  B  passes  the 
position  A,  and  A  passes  the  position  B,  the  direction  of  the  E.  M. 

F.  in  B  and  in  A,  and  consequently  the  direction  of  the  current  in 
the  coil,  is  reversed,  but  at  this  same  instant  the  opposite  face  of 
the  coil  is  presented  to  P,  so  that  viewed  from  P,  the  current 
flowing  around  the  coil  is  always  in  the  same  direction.    This  cur- 
rent is  pulsating.     It  is  zero  when  the  plane  of  the  coil  is  at  right 
angles  to  the  magnetic  meridian,  and  it  is  a  maximum  when  this 
plane  coincides  with  the  meridian,  hence  it  rises  and  falls  with 
every  half  revolution  of  the  coil.    At  the  instant  when  the  plane 
of  the  coil  coincides  with  the  magnetic  meridian,  the  instrument 
is  in  principle  the  same  as  a  tangent  galvanometer  (Par.  373), 
and  at  all  times  it  may  be  regarded  as  a  tangent  galvanometer 
traversed  by  a  current  whose  value  is  a  mean  of  the  instantane- 
ous values  of  the  current.    The  suspended  needle  will  be  deflected 
accordingly. 

The  induced  E.  M.  F.  will  vary  directly  with  the  rate  of  cutting 
of  the  lines  of  force  embraced  by  the  coil.  The  number  embraced 
is  Trr2H,  r  being  the  mean  radius  of  the  coil.  The  rate  at  which 
these  are  cut  varies  with  «,  the  angular  velocity  of  the  coil,  and 
with  n,  the  number  of  turns  in  the  coil.  If  R  be  the  resistance  of 
the  coil,  the  current  through  it  is  proportional  to 


The  field  produced  at  the  center  of  the  coil  is  (Par.  354) 
/  _  T  v  2wn  -  27r2r#ra2co 

J~~  1  x~r     ~w~ 

If  the  needle  be  deflected  through  an  angle  6,  we  have  (Par.  146) 


whence 

,-> 

•ft   = 

tan  5 


ELECTRO-MAGNETICS.  429 

But  rco  is  the  actual  velocity  of  a  point  at  the  extremity  of  the 
horizontal  diameter  of  the  coil.    Calling  this  v,  we  have 


D 

R  =  r  -  -.V 

tan  6 

whence  we  see  that  the  resist- 

ance of  the  coil  is  equal  to  the  product  of  a  velocity  by  a  numerical 
factor.  In  the  expression  above,  n  and  r  are  constants  of  the  in- 
strument and  w  and  5  are  determined  by  observation.  It  will  be 
noted  that  it  is  not  necessary  to  know  the  strength  of  the  needle  or 
the  intensity  of  the  field  H.  If  v  be  expressed  in  centimeters  per 
second,  R  will  be  in  absolute  units  of  resistance. 

In  actually  carrying  out  the  above  determination,  many 
delicate  refinements  were  observed.  These  are  described  in  detail 
in  the  Report  of  the  British  Association  for  the  Advancement  of 
Science  for  the  year  1864. 

Resistance  has  been  measured  absolutely  by  several  other 
methods. 

543.  The  Ohm.  —  As  a  result  of  the  experiment  outlined  in  the 
preceding  paragraph,  the  investigators  became  possessed  of  a  coil 
of  wire  whose  resistance  in  absolute  units  was  accurately  known. 
The  absolute  unit  being  excessively  small,  the  next  step  was  to 
select  a  practical  unit  which  should  be  based  upon  this  absolute 
unit.    It  has  been  shown  (Par.  284)  that  the  need  for  a  unit  of 
resistance  had  been  felt  for  some  time.    The  resistance  coils  made 
by  Ohm  could  not  be  standardized.    In  1860  Siemens  defined  as 
a  unit  of  resistance  a  column  of  pure  mercury  one  meter  long  and 
one  square  millimeter  in  cross-section,  the  mercury  being  at  a 
temperature  of  0°  C.     Electricians  had  become  accustomed  to 
this  unit  and  the  German  scientists  especially  were  loath  to  give 
it  up.    The  practical  unit  of  resistance,  the  ohm,  was  accordingly 
chosen  so  as  to  agree  as  nearly  as  possible  with  Siemen's  unit,  and 
was  defined  as  109  absolute  units  of  resistance,  or  (Par.  291)  as 
the  resistance  of  a  column  of  mercury,  one  millimeter  in  cross- 
section  and  106.3  centimeters  in  length,  at  a  temperature  of  0°  C. 
It  was  later  found  more  convenient  to  retain  the  length  of  the 
column  but  to  specify  the  quantity  of  mercury  in  terms  of  weight, 
or  as  14.4521  grams. 

544.  The  Ampere.  —  We  have  seen  above  (Par.  538)  that  the 
absolute  unit  of  current  had  been  determined  from  the  tangent 


430  ELEMENTS  OF  ELECTRICITY. 

galvanometer.  It  remains  now  to  fix  the  practical  unit  of  current. 
The  existing  practical  standard  of  E.  M.  F.  was  that  of  the  Daniell 
cell  (Par.  206).  This  applied  to  the  practical  unit  of  resistance, 
the  ohm,  should  drive  through  it  the  unit  current.  This  current 
was  found  to  be  very  nearly  one-tenth  of  the  absolute  unit.  The 
practical  unit  of  current,  the  ampere,  was  therefore  selected  as 
exactly  one-tenth  of  the  absolute  unit.  Its  definition  has  already 
been  given  (Par.  228). 

545.  The  Volt. — The  selection  of  the  primary  practical  units 
of  resistance  and  current  also  fixed  the  volt,  the  practical  unit  of 
E.  M.  F.    From  Ohm's  law,  E  =  IR.    Since  /  =  1Q-1  absolute  units 
of  current  and  #  =  109  absolute  units  of  resistance,  £'  =  10-1Xl09 
=  108.    The  volt  was  therefore  defined  as  108  absolute  units  of 
E.  M.  F. 

546.  Resume. — The  following  resume  will  show  the  thread  of 
connection  between  the  successive  steps  in  the  adoption  of  the 
absolute  and  the  practical  electro-magnetic  units. 

(a)  The  absolute  unit  of  current  was  determined  by  means  of 
the  tangent  galvanometer. 

(b)  The  absolute  resistance  of  a  coil  of  wire  was  determined  by 
rotating  the  coil. 

(c)  From  this  was  determined  the  absolute  unit  of  resistance. 

(d)  This  was  found  to  be  about  .954  XlO~ 9  of  Siemen's  mercury 
unit,  already  in  use. 

(e)  To  disturb  this  standard  as  little  as  possible,  the  practical 
unit  of  resistance,  the  ohm,  was  taken  as  109  absolute  units  of 
resistance. 

(f)  The  existing  practical  standard  of  E.  M.  F.  was  that  of  the 
Daniell  cell  (1.07  volts)  and  it  was  desirable  to  disturb  this  as 
little  as  possible. 

(g)  A  Daniell  cell  applied  to  a  circuit  of  one  ohm  drove  through 
it  a  current  which  was  very  slightly  greater  than  one-tenth  of  the 
absolute  unit-  of  current. 

(h)  The  practical  unit  of  current,  the  ampere,  was  taken  as 
exactly  one-tenth  of  the  absolute  unit  of  current. 

(i)  The  selection  of  the  practical  units  of  resistance  and  current 
involved  that  of  E.  M.  F.,  the  volt,  since  the  three  units  are 
bound  together  by  Ohm's  law.  The  volt  is,  therefore,  108  absolute 
units  of  E.  M.  F. 


ELECTRO-MAGNETICS.  431 

547.  Comparison  of  the  Dimensional  Formulae  in  the  Two 
Systems.  —  A  comparison  of  the  dimensional  formulae  of  the  units 
in  the  two  systems  will  point  to  the  contradictory  conclusion  that 
they  do  not  agree.  As  an  example,  let  us  compare  the  dimensional 
formulae  of  the  units  of  quantity. 

In  the  electro-static  system,  we  have  from  Coulomb's  laws  for 
the  force  exerted  between  Jtwo  equal  quantities  Q  (Par.  56), 
F  =  Q*/L2,  whence  Q  =  L  vF.  In  mechanics  it  is  shown  that 
force  =  mass  X  acceleration,  or  F=MxL/T2.  Substituting  this 
value  of  F  in  the  expression  above,  we  have  for  the  electro-static 
dimensional  formula  of  quantity 

(I) 


In  the  electro-magnetic  system,  Q  =  IxT  =  (E/R)xT.  In 
Par.  540  it  was  shown  that  E=FxL/Q  and  that  R  =  L/T, 
whence  the  electro-magnetic  dimensional  formula  of  quantity  is 

Q=VALL  (ii) 

Comparing  (I)  and  (II),  we  see  at  once  that  they  are  not  the 
same,  and  that  the  ratio  of  (I)  to  (II)  is  L/T,  a  velocity. 

In  a  similar  manner  may  be  determined  the  dimensional 
formulae  of  the  remaining  units  of  current,  capacity,  potential 
resistance,  and  inductance  as  given  in  the  following  table: 

Unit  Electro-static  Electro-magnetic          Ratio 

Current  LVW2./T*  VluTL/T  L/T  =  V 

Quantity  LVM.L/T  v^LL  L/T  =  V 

Capacity  L  TZ/L  L*/T*  =  V* 

Potential  VWX/T  LVM.L/T2  T/L  =  l/V 

Resistance  T/L  L/T  T*/L*  =  1/V* 

Inductance  T2/L  L  T2/L2  =  1/V2 

The  V  which  enters  all  of  these  ratios  has  been  determined  in 
widely  different  ways  by  a  number  of  observers  and  found  to  be 
3xl010,  or  thirty  billion,  centimeters  per  second.  This  is  the 
velocity  of  light. 

548.  Explanation  of  Lack  of  Agreement.  —  It  is  on  the  face  of 
it  absurd  that  like  quantities  should  have  different  dimensional 
formulae,  and  also  that  these  formulae  should  contain  such 
irrational  quantities  as  the  square  root  of  a  mass  and  of  a  length. 
Consideration  will  show  that  this  state  of  affairs  results  from  our 
failure  to  take  into  account  in  the  formulae  above  the  dielectric 


432  ELEMENTS  OF  ELECTRICITY. 

coefficient  K  (Par.  90)  in  the  case  of  the  electro-static  units,  and 
the  permeability  /*  (Par.  392)  in  the  case  of  the  electro-magnetic 
units.  The  medium  being  air,  these  factors  are  both  unity  and 
hence  are  of  no  arithmetical  effect,  but  in  omitting  them  we  are 
not  justified  in  ignoring  their  dimensions.  What  these  dimensions 
are,  we  do  not  know,  but  that-  they  account  for  the  lack  of  agree- 
ment in  the  dimensional  formulae  of  the  two  systems  the  following 
will  show. 

In  the  preceding  paragraph,  in  determining  the  dimensional 
formula  of  the  electro-static  unit  of  quantity,  our  assumed  ex- 
pression for  the  force  between  two  equal  quantities  Q  should  have 
been  (Par.  90)  F=Q*/K.L2 

whence  Q  =  L^/K.VMJ./T  (I) 

Likewise,  in  determining  the  dimensional  formula  of  the  electro- 
magnetic unit  of  quantity,  the  expression  for  the  force  between 
two  equal  magnetic  poles  should  have  been  (Par.  133) 

Whence  m 

The  force  exerted  by  a  current  /,  flowing  in  a  circular  coil  of 
radius  L,  upon  a  pole  m  at  the  center  of  the  coil  is  proportional  to 
ml/L  (Par.  355),  whence 

/  =  F.L/m 

Substituting  the  value  of  m  above  and  multiplying  by  T,  we 
have,  since  Q  =  IxT  _ 

Q  =  VM.L/VV  (ii) 

Equating  the  second  members  of  (I)  and  (II)  and  solving 


T 

We  see  then  that  while  the  dimensions  of  the  separate  factors 
K  and  n  are  unknown,  the  reciprocal  of  the  square  root  of  their 
product  is  a  velocity,  and  therefore  they  can  not  be  disregarded. 

This  velocity,  as  stated  in  the  preceding  paragraph,  is  the 
velocity  of  light,  and  is  also  the  velocity  with  which  electric 
waves  travel  through  space.  As  will  be  shown  later  it  has  an 
important  bearing  on  Maxwell's  electro-magnetic  theory  of  light, 
which  is  that  light  is  really  due  to  the  passage  of  electric  waves 
through  the  ether. 


ELECTRO-MECHANICS.  433 


PART  V. 
ELECTRO-MECHANICS. 


CHAPTER  40. 

DIRECT   CURRENT   GENERATORS. 

549.  Electro-Mechanics. — Electro-Mechanics,  the  subject  which 
we  are  now  to  take  up,  is  a  more  or  less  artificial  division  in- 
tended to  embrace  the  production  of  electric  currents  by  machin- 
ery, a  consideration  of  these  mechanically  generated  currents,  and 
finally  their  employment  to  operate  other  machines. 

Electricity,  no  matter  how  produced,  is  always  the  same  agent 
and  the  principles  which  have  been  developed  in  the  preceding 
pages  suffice  to  explain  all  the  facts  which  we  shall  now  bring  out. 
The  currents  produced  by  machines  are,  however,  more  or  less 
pulsating  and  are  often  alternating,  that  is,  they  periodically 
(usually  many  times  a  second),  change  their  direction.  These 
rapid  changes  in  the  current  give  rise  to  certain  phenomena  which 
renders  it  desirable  to  consider  these  currents  in  detail. 

550.  Classes  of  Electrical  Machines. — Electrical  machines  are 
primarily  of  two  classes,  generators  and  motors.    The  former,  also 
called  dynamos,  transform  mechanical  energy  into  electrical  energy 
and  therefore  deliver  electrical  energy  to  a  circuit.    On  the  other 
hand,  motors  transform  electrical  energy  into  mechanical  energy 
and  therefore  receive  electrical  energy  from  a  circuit. 

Machines  are  further  classed  according  as  they  are  designed  to 
deal  with  direct  currents  or  with  alternating  currents.  We  shall 
now  consider  generators  of  the  former  class. 

551.  Coil  Rotating  in  a  Magnetic  Field.— Suppose  CD,  Fig.  262, 
to  be  a  coil  in  the  magnetic  field  NS  and  free  to  rotate  about  the 
axis  A  B.    Suppose  its  initial  position  to  be,  as  shown  in  the  figure, 
with  its  plane  perpendicular  to  the  lines  of  force  of  the  field.    It 


434 


ELEMENTS  OF  ELECTRICITY. 


now  embraces  the  maximum  number  of  these  lines,  and  the  first 
effect  of  rotation  about  AB,  whether  clockwise  or  counter-clock- 
wise, will  be  to  decrease  this  number.  This  change  will  develop 
in  the  coil  an  induced  E.  M.  F.  whose  direction  may  be  determined 
by  application  of  the  rule  given  in  Par.  421.  It  is  simpler,  however, 
to  apply  the  right  hand  rule  given  in  Par.  422,  whence  we  see  at 
once  that  whether  the  rotation  be  clockwise  or  counter-clockwise, 
as  the  side  C  of  the  coil  rotates  180°  from  the  position  C  to  the 


Fig.  262. 

position  D,  there  is  an  E.  M.  F.  induced  in  C  from  rear  to  front, 
while  as  it  rotates  from  D  to  (7,  the  E.  M.  F.  induced  is  from  front 
to  rear.  The  E.  M.  F.  is  reversed  in  direction  whenever  the  coil 
passes  through  the  perpendicular  plane,  and  is  zero  when  the 
coil  lies  in  it,  for  which  reason  this  plane  is  called  the  neutral 
plane. 

552.  Calculation  of  E.  M.  F.  of  Rotating  Coil.— The  E.  M.  F. 

induced  by  the  rotation  of  a  coil  in  a  magnetic  field  is  from  Par. 
426  equal  to  the  rate  of  decrease  of  the  number  of  lines  of  force 
embraced  by  the  coil.  If  the  field  be  uniform,  this  E.  M.  F.  may 
be  calculated  as  follows.  Let  ab,  Fig.  263,  be  the  primary  position 
of  the  coil,  its  plane  at  right  angles  to  the  field.  Its  E.  M.  F.  at 
any  point,  such  as  d,  is  measured  by  the  rate  of  decrease  at  that 
point  of  the  number  of  lines  embraced. 

Let  the  total  field  embraced  by  ab  be  N.  Let  the  coil  make  n 
revolutions  per  second,  that  is,  let  its  angular  velocity  be  2vn. 
If  ca,  the  radius  of  the  circle  described  by  a,  be  R,  the  actual 
velocity  of  a  is  2irnR  per  second.  At  h  the  coil  is  moving  at  right 
angles  across  the  field  with  a  velocity  which  in  one  second  would 


ELECTRO-MECHANICS. 


435 


carry  it  a  distance  hk.    The  total  width  of  the  field  being  2R,  it 


would  be  crossed  in 


=  —  seconds,  and  in  this  time  N  lines 


of  force  would  be  cut  by  each  side  of  the  coil,  therefore,  the  E.  M.  F. 
being  generated  at  h  is 

9  \7 

-       E=^  =  2™N 

a 


fer 


i                 lia 

\                    '    \                        . 

\                    '      \                            1 

\               •'         1                           ' 

:g: 


b 

Fig.  263. 

If  the  coil  consists  of  S  turns,  the  E.  M.  F.  is  2-jrnNS.  To  con- 
vert this  to  volts,  it  must  be  divided  by  108  (Par.  427),  whence 
finally 

volts. 


Should  the  coil  at  d  continue  to  move  for  one  second  in  the 
same  direction  and  at  the  same  rate  as  at  d,  it  would  move  a  dis- 
tance de=hk  and  in  doing  so  would  cut  across  the  lines  between 
/  and  e.  If  the  angle  dca  through  which  the  coil  has  turned  from 
its  primary  position  be  0,  then  fe=de.  sin  6.  At  the  same  time, 
the  other  side  g  of  the  coil  is  cutting  across  the  field  at  this  same 
rate,  the  total  decrease  being  2de.  sin  d.  Since  de=hk,  the  E.  M.  F. 
being  generated  at  d  is 

2mrNS    .     . 


Or  placing  C  for  the  coefficient  of  sin  0, 

E=C.  sin  0 

For  the  present  it  is  sufficient  to  bear  in  mind  that  the  E.  M.  F. 
generated  by  a  coil  rotating  in  a  uniform  field  varies  as  the  sine 
of  the  angle  through  which  the  coil  has  turned  from  its  primary 
position  at  right  angles  to  the  field,  that  is,  from  the  neutral  plane. 


436 


ELEMENTS  OF  ELECTRICITY. 


553.  Production  of  Current  by  Rotating  Coil.— In  Fig.  264  let 
CD  represent  a  coil  rotating  about  the  axis  XY  in  the  magnetic 
field  NS,  and  suppose  that  instead  of  being  a  closed  coil,  the  end 
C  terminates  in  a  ring  A,  and  the  end  D  in  a  ring  B,  these  rings 
being  attached  to  the  axis  upon  which  the  coil  rotates,  but  being 
insulated  from  it  and  from  each  other.  In  Par.  551  it  was  shown 
that  as  the  coil  rotates  180°  from  its  present  position  at  right 


Fig.  264. 

angles  to  the  field,  an  E.  M.  F.  is  generated  from  rear  to  front  in  C 
and  from  front  to  rear  in  D.  No  current  is  produced  because  the 
circuit  is  broken  between  the  rings.  If  now  a  metal  strip  E  be 
pressed  against  the  ring  A,  and  a  second  strip  F  be  pressed  against 
B,  and  these  strips  be  connected  by  a  wire,  the  circuit  will  be 
completed  and  a  current  will  flow  through  the  coil  and  wire  as 
indicated  by  the  arrows.  A  and  B  are  collector  rings,  E  and  F  are 
brushes,  and  the  wire  connecting  these  brushes  is  the  external 
circuit. 

554.  Alternating  Current. — The  resistance  of  the  arrangement 
just  described  being  constant,  the  current  in  the  external  circuit 
varies  directly  with  the  E.  M.  F.  generated  in  the  coil  and  this, 
we  have  seen  (Par.  552),  varies  as  the  sine  of  the  angle  through 
which  the  coil  has  rotated  from  its  position  in  the  neutral  plane. 


ELECTRO-MECHANICS. 


437 


Thus,  at  the  instant  shown  in  Fig.  264,  the  current  in  C  is  zero, 
but  as  C  moves,  a  current  flows  towards  A,  reaching  its  maximum 
value  when  the  coil  has  turned  through  90°  or  has  become  parallel 
to  the  lines  of  force  of  the  field.  From  this  point,  the  current 
diminishes  and  is  again  zero  when  C  has  turned  through  180°  or 
has  reached  the  position  D.  As  C  passes  this  point,  the  current 
again  starts  up,  but  it  is  now  reversed,  that  is,  it  flows  away  from 
instead  of  towards  A,  and  it  consequently  is  also  reversed  in  the 
external  circuit.  If  the  original  direction  be  considered  positive, 
this  last  must  be  considered  negative.  The  current  therefore 
reaches  a  negative  maximum  when  C  has  turned  through  270°, 
returns  to  zero  when  C  reaches  its  primary  position,  and  again 
reverses  as  C  passes  through  this  position. 

To  an  E.  M.  F.  and  current  which  thus  pass  through  these 
periodic  fluctuations  and  reversals,  the  term  alternating  is  applied. 

555.  Graphic  Representation  of  Alternating  E.  M.  F.  and  Cur- 
rent.— In  Fig.  265  let  B  represent  the  cross-section  of  a  coil  rotat- 
ing about  0  as  a  center  and  in  a  uniform  field  whose  positive 


Fig.  265. 


direction,  as  indicated  by  the  arrows,  is  downwards.  AD  is  there- 
fore the  neutral  plane.  Should  the  coil  start  at  A,  the  direction 
of  the  induced  E.  M.  F.  is  independent  of  the  direction  of  rotation, 
that  is,  whether  the  coil  rotates  in  a  clockwise  or  in  a  counter- 
clockwise direction,  the  E.  M.  F.  will  act  out  from  the  plane  of  the 
paper.  However,  to  conform  to  the  trigonometric  convention  as 
to  the  direction  in  which  angles  are  to  be  measured,  we  shall 
assume  the  rotation  to  be  counter-clockwise.  From  Par.  552,  the 
induced  E.  M.  F.  at  any  point  B  is  proportional  to  B  N,  the  sine 
of  the  angle  6  through  which  the  coil  has  rotated.  If,  therefore, 
we  lay  off  on  a  horizontal  axis,  A  A,  distances  proportional  to  the 


438  ELEMENTS  OF  ELECTRICITY. 

angles  through  which  the  coil  has  turned,  and  at  the  points  so 
determined  erect  ordinates  upon  which  we  lay  off  distances  pro- 
portional to  the  sines  of  the  corresponding  angles,  the  sine  or 
harmonic  curve  drawn  through  the  extremities  of  these  ordinates 
will  represent  the  successive  values  of  the  E.  M.  F.  For  example, 
the  point  R  is  determined  by  laying  off  AM  proportional  to  AB, 
and  MR  proportional  (in  this  case  equal)  to  NB. 

The  curve  shows  what  was  stated  in  the  preceding  paragraph, 
that  is,  that  the  E.  M.  F.  is  zero  at  A,  rises  to  a  maximum  when  the 
coil  reaches  C,  decreases  to  zero  at  D  where  it  reverses,  reaches  a 
negative  maximum  at  E  and  returns  to  zero  at  A,  and  so  on. 

In  the  case  under  consideration,  the  E.  M.  F.  acting  towards 
the  observer  is  considered  positive,  but  this  is  purely  a  matter  of 
convention  and  it  is  immaterial  whether  we  regard  it  as  positive 
or  negative  provided  that  the  E.  M.  F.  induced  as  the  coil  rotates 
from  A  to  D  be  opposite  in  sign  to  that  induced  as  it  rotates  from 
D  to  A.  If  the  direction  of  the  field  be  reversed,  the  direction  of 
the  E.  M.  F.  is  also  reversed. 

Since  the  current  varies  directly  with  the  E.  M.  F.,  we  may  take 
this  same  sine  curve  as  representing  the  current  also,  or  we  may 
represent  the  current  by  another  sine  curve  of  the  same  periodicity 
but  of  different  amplitude.  From  Ohm's  law,  I=E/R,  we  see 
that  /  and  E  are  numerically  equal  only  when  R  is  unity.  If  R 
be  less  than  unity,  /  is  numerically  greater  than  E  and  would  be 
represented  by  the  outer  broken  curve  in  Fig.  265.  If  R  be  greater 
than  unity,  /  would  be  represented  by  the  inner  broken  curve. 

Reflection  will  show  that  the  abscissae  of  these  sine  curves  may 
also  be  laid  off  on  a  scale  of  time,  the  distance  A  A  corresponding 
to  the  time  of  one  complete  revolution  of  the  coil. 

556.  Rectification  of  Alternating  Current. — Fig.  266  represents 
the  same  arrangement  of  a  coil  rotating  in  a  magnetic  field  as 
described  in  Par.  553,  only  in  this  case  the  ends  of  the  coil  termi- 
nate in  the  copper  semicircles  or  segments  A  and  B  instead  of  in 
two  separate  rings.  These  segments  are  likewise  mounted  upon 
the  shaft  of  the  coil,  insulated  from  it  and  from  each  other.  The 
brush  E  presses  against  the  segment  A;  the  brush  F  against  the 
segment  B.  For  simplicity  of  description,  suppose  the  rotation 
to  be  clockwise.  As  C  moves  from  its  present  position  to  the 
position  D,  the  induced  E.  M.  F.  acts  towards  A,  and  current  will 
therefore  enter  the  external  circuit  by  the  brush  E  and  leave  it 


ELECTRO-MECHANICS. 


439 


by  the  brush  F.  As  C,  having  reached  the  position  D,  passes 
through  the  neutral  plane,  the  induced  E.  M.  F.  becomes  zero 
and  immediately  thereafter  reverses,  that  is,  acts  from  A  and 


Fig.  266. 

towards  B.  But  also,  as  the  coil  passes  through  the  neutral  plane 
the  brushes  slip  across  the  gap  between  the  segments  and  E  is 
now  in  contact  with  B,  while  F  is  in  contact  with  A,  therefore, 


Fig.  267. 

current  still  flows  out  into  the  external  circuit  through  the  brush 
E  and  the  direction  of  the  current  in  the  external  circuit  remains 
unchanged. 


440  ELEMENTS  OF  ELECTRICITY. 

This  is  shown  graphically  in  Fig.  267.  The  sine  curve  A  repre- 
sents the  alternating  current  (and  E.  M.  F.)  in  the  coil.  B 
represents  the  current  in  the  external  circuit,  the  negative  loops 
of  the  curve  A  having  been  reversed  and  made  positive. 

An  alternating  current  which  has  thus  been  made  unidirectional 
is  said  to  be  rectified.  The  split  ring,  or  arrangement  of  copper 
segments  by  which  this  is  brought  about,  is  a  commutator,  and  the 
process  is  called  commutation  or  rectification.  We  shall  see  later 
that  an  alternating  current  may  be  rectified  otherwise  than  by  a 
commutator. 

557.  Increase  in  Number  of  Turns  of  Coil. — If  the  rotating 
coil,  instead  of  consisting  of  a  single  turn,  be  composed  of  several 


Fig.  268. 

as  shown  in  Fig.  268,  an  approximately  equal  E.  M.  F.  will  be 
induced  in  each.  Examination  of  the  figure  will  show  that  these 
turns  being  connected  in  series,  the  total  E.  M.  F.  is  the  sum  of 
the  separate  E.  M.  F.s,  or  increases  in  proportion  to  the  number 
of  turns.  The  resultant  E.  M.  F.  of  the  coil  is  represented  graph- 
ically by  a  sine  curve  of  the  same  periodicity  as  the  curves  in  Fig. 
267  but  of  an  amplitude  greater  in  proportion  to  the  number  of 
turns. 

Although  the  E.  M.  F.  is  thus  increased  by  increasing  the 
number  of  turns,  practical  considerations  place  a  limit  upon  the 
number  that  may  be  added.  Thus,  the  resistance  of  the  coil 
increases  directly  with  the  number  of  turns  and  it  is  important 
that  this  resistance  should  be  kept  very  small.  The  diameter  of 
the  wire,  already  large,  must  therefore  be  increased,  and  the  wire 
is  further  enlarged  by  an  insulating  covering.  In  the  actual 


ELECTRO-MECHANICS. 


441 


machines,  the  space  in  which  these  wires  are  wound  is  restricted, 
being  usually  a  narrow  groove  or  slot  in  the  surface  of  a  cylindrical 
body,  and  therefore  the  number  of  turns  seldom  exceeds  six  or 
eight. 

558.  Increase  in  Number  of  Coils. — For  a  considerable  portion 
of  the  time  during  the  rotation  of  the  single  coil  described  in  the 
preceding  paragraphs,  the  induced  E.  M.  F.  is  small,  and  twice 
during  each  complete  revolution  it  is  zero.  If  there  be  mounted 
upon  the  same  axis  a  second  coil  whose  plane  is  at  right  angles  to 
that  of  the  first  (Fig.  269),  the  induced  E.  M.  F.  in  this  second 


Fig,  269. 

coil  will  be  a  maximum  at  the  instant  when  it  is  zero  in  the  first 
coil,  and  also  it  will  be  zero  in  the  second  coil  when  it  is  a  maximum 
in  the  first.  By  a  suitably  arranged  commutator  we  may  always 
draw  current  from  that  coil  whose  E.  M.  F.  is  the  greater,  and 
thus  avoid  the  periodic  dropping  to  zero.  For  example,  suppose 
the  commutator  to  consist  of  four  segments  to  which  the  coils  are 
connected  as  indicated  in  the  figure.  At  the  instant  represented, 
the  E.  M.  F.  in  A  A,  the  vertical  coil,  is  zero,  and  that  in  BB,  the 
horizontal  coil,  is  a  maximum,  and  it  is  this  latter  coil  which  is 
sending  current  out  into  the  external  circuit.  As  the  coils  rotate, 
the  E.  M.  F.  in  BB  decreases,  that  in  AA  increases,  and  these 
reach  equality  when  the  coils  have  turned  through  an  angle  of  45°. 
At  that  moment,  the  brushes  are  across  the  gap  between  the  seg- 
ments and  in  contact  with  both.  At  the  next  instant,  the  brushes 
are  in  contact  with  the  segments  connected  to  the  A  A  coil,  in 
which  coil  the  E.  M.  F.  is  rising  to  a  maximum.  These  changes 


442 


ELEMENTS  OF  ELECTRICITY. 


are  shown  graphically  in  Fig.  270.  The  broken  and  dotted  curve 
represents  the  rectified  E.  M.  F.  in  the  BE  coil;  the  broken  curve 
represents  the  same  in  the  AA  coil.  The  maxima  follow  at  inter- 
vals of  90°  and  midway  between  these  maxima,  as  indicated  by 
the  intersection  of  the  curves,  the  E.  M.  F.s  are  equal.  The 
unbroken  portion  of  these  curves  represents  the  E.  M.  F.  (and 


Fig.  270. 

current)  in  the  external  circuit.  We  therefore  see  that  by  inserting 
the  second  coil  we  obtain  a  current  which,  while  pulsating,  does 
not  drop  to  zero  as  did  the  current  from  the  original  coil.  If  still 
other  coils  be  inserted  between  these  two,  we  may  obtain  a  cur- 
rent which  fluctuates  less  and  less,  and  approaches  constancy  as 
the  number  of  coils  is  increased. 

559.  Open  and  Closed  Coils. — Consideration  of  Fig.  269  will 
reveal  the  fact  that  except  for  the  very  brief  instant  when  the 
brushes  slide  across  the  gap  between  the  commutator  segments, 
only  one  coil  at  a  time  supplies  current  to  the  external  circuit. 
Thus,  while  the  coil  BB  is  supplying  current,  the  coil  A  A  is  open 
at  the  commutator  end  and  contributes  nothing.  The  E.  M.  F. 
induced  in  these  coils  while  the  corresponding  commutator  seg- 
ments are  not  in  contact  with  the  brushes  is  represented  by  the 
broken  portions  of  the  curves  in  Fig.  270.  This  E.  M.  F.  is  not 
utilized.  An  arrangement  in  this  manner  of  the  coils  of  a  generator 
is  called  an  open-coil  winding. 


R 


Fig.  271. 

We  shall  shortly  see  (Par.  569)  that  there  is  possible  another 
arrangement  by  which  the  various  coils  may  be  connected  in 
series  and  thus  instead  of  being  idle  during  a  portion  of  the  rotation 
they  all  constantly  contribute  to  a  resultant  E.  M.  F.  This  ar- 


ELECTRO-MECHANICS.  443 

rangement  is  called  a  closed-coil  winding.  Points  on  the  curve 
RR',  Fig.  271,  representing  this  resultant  E.  M.  F.  are  obtained 
by  adding  the  corresponding  ordinates  of  the  component  curves. 
It  is  seen  that  as  the  number  of  coils  is  increased,  not  only 
does  the  resultant  E.  M.  F.  increase  but  also  the  loops  in  the 
curve  RR'  become  greater  in  number  and  smaller  in  amplitude, 
that  is,  the  E.  M.  F.  becomes  less  pulsating  and  more  nearly 
constant. 

560.  Essential  Parts  of  D.  C.  Generator. — The  essential  parts 
of  a  D.  C.  generator  are — 

(a)  A  magnetic  field. 

(b)  Rotating  coils. 

(c)  A  commutator. 

(d)  Brushes. 

The  coils  and  commutator  and  the  shaft  to  which  they  are 
attached  and  with  which  they  rotate  are  known  collectively  as 
the  armature.  The  coils  are  usually  inserted  in  grooves  or  slots 
in  an  enlarged  portion  of  the  shaft  called  the  armature  core.  The 
portions  of  the  coils  on  the  exterior  of  the  armature  core  and 
parallel  to  the  axis  of  the  shaft  are  called  inductors. 

561.  The  Field. — The  magnetic  field  in  which  the  armature 
revolves  is  produced  by  field  magnets,  which  may  be  either  per- 
manent or  electro-magnets.     Permanent  magnets  can  not  be 
controlled  nor  can  they  be  made  of  the  size  and  strength  required 
in  large  machines  and  they  are  therefore  restricted  to  such  small 
generators  as  those  used  to  operate  the  call  bell  of  a  telephone  or 
the  sparking  apparatus  of  a  gasoline  engine.     In  all  important 
generators,  electro-magnets  are  employed.    It  is  to  this  class  of 
generators  that  we  refer  in  the  following  pages. 

Whatever  be  the  external  appearance  of  the  generator,  analysis 
will  show  that  the  field  magnets  are  in  principle  horseshoe  magnets, 
each  consisting  of  a  yoke  and  two  limbs,  the  ends  of  these  latter 
being  shaped  to  embrace  between  them  the  revolving  armature. 
The  field  coils  are  wrapped  about  these  limbs,  or  magnet  cores. 
In  the  simplest  form  of  generator,  as  shown  in  Fig.  273,  there  are 
but  two  magnet  cores  and  the  machine  is  designated  as  bipolar. 
If  there  be  more  than  one  pair  of  cores,  the  machine  is  multipolar. 
Whatever  be  the  number  of  poles,  they  are  alternately  north  and 


444 


ELEMENTS  OF  ELECTRICITY. 


south.  Fig.  272  represents  the  frame  of  a  multipolar  generator 
of  six  poles.  It  will  be  seen  that  a  similar  arrangement  would 
result  by  grouping  around  a  common  center  six  horseshoe  mag- 
nets, the  like  poles  of  adjacent  magnets  being  side  by  side. 


YOKE 


Fig.  272. 

The  magnet  cores  are  made  of  soft  annealed  steel  so  as  to  be 
free  from  hysteresis.  They  are  frequently  laminated  so  as  to 
avoid  eddy  currents.  They  terminate  in  soft  iron  pieces,  shoes, 
which  perform  several  functions,  (a)  They  hold  in  position  the 
field  coils  after  these  latter  have  been  slipped  over  the  cores,  (b) 
They  diminish  the  air  gap  between  the  pole  faces  and  the  armature 
core,  (c)  By  the  shape  of  their  ends,  or  horns,  they  produce  an 
advantageous  distribution  of  the  flux. 

562.  Excitation  of  Field  Magnets.— For  all  D.  C.  generators  the 
field  magnets  are  self-excited,  that  is,  they  are  excited  by  current 
from  the  machine  itself. 

Since  the  machine  will  not  generate  a  current  unless  the  field 
be  excited,  and  since  the  field  is  excited  by  the  current  drawn  from 


ELECTRO-MECHANICS. 


445 


the  machine  itself,  it  is  not  clear  at  first  sight  why  a  generator 
ever  produces  a  current.  If  the  field  magnets  were  of  perfectly 
pure  soft  iron,  it  is  probable  that  no  current  would  be  produced 
when  the  generator  was  set  in  motion,  but  the  iron  is  not  per- 
fectly pure  and  there  is  always  some  slight  residual  magnetism 
left  in  the  cores  (Par.  155),  and  when  the  machine  is  started, 
this  is  sufficient  to  produce  a  small  current  through  the  field 
coils.  This  strengthens  the  magnets  which  in  turn  increases  the 
current,  and  so  on,  a  generator  on  starting  "building  up"  grad- 
ually, and  frequently  taking  a  minute  or  so  to  reach  normal  out- 
put. This  building  up  may  sometimes  be  aided  by  the  earth's 
field. 

563.  Methods  of  Self-Excitation. — There  are  three  distinct 
ways  in  which  the  coils  of  the  field  magnets  may  be  wound  and 
the  exciting  current  passed  through  them  so  as  to  obtain  the 
desired  number  of  ampere  turns.  The  corresponding  generators 
are  said  to  be  series  wound,  shunt  wound,  and  compound  wound 
respectively. 

In  a  series-wound  generator,  the  entire  current  passes  through 
the  field  coils/  In  Fig.  273,  a  represents  diagrammatically  a 


Fig.  273. 

series-wound,  bipolar  machine.  The  same  current  which  passes 
through  the  field  coils  flows  through  the  external  circuit,  or  the 
field  coils  and  the  external  circuit  are  in  series.  A  still  more 
highly  conventionalized  diagram  of  the  same  machine  is  repre- 
sented in  6. 

In  a  shunt-wound  generator,  only  a  portion  of  the  entire  current, 
from  two  to  ten  per  cent,  is  passed  through  the  field  coils.  These 
coils  are  therefore  in  shunt  with  the  external  circuit.  In  Fig.  274, 


446 


ELEMENTS  OF  ELECTRICITY. 


a  represents  a  shunt-wound,  bipolar  machine,  the  shunt  being 
indicated  by  the  dotted  line,  and  b  is  a  more  conventionalized 
diagram  of  the  same  machine.  Since  only  a  fraction  of  the  entire 
current  passes  through  the  field  coils,  in  order  to  secure  the  neces- 
sary ampere  turns  for  the  excitation  of  the  magnet  cores,  there 
must  be  many  more  turns  in  these  coils  than  in  the  case  of  those  of 
a  series-wound  machine. 


Fig.  274. 

The  field  coils  of  a  compound-wound  machine  combine  series 
and  shunt  windings.  Thus  in  Fig.  275,  a  represents  a  compound- 
wound,  bipolar  machine,  the  series  winding  being  shown  by  the 
heavy  line  and  the  shunt  winding  by  the  dotted  line.  For  clearness 
of  the  diagram,  the  windings  are  represented  as  on  separate  por- 
tions of  the  cores. 


Fig.  275. 

There  are  two  varieties  of  the  compound  windings,  known  as 
compound  short  shunt  and  compound  long  shunt.  If  the  shunt  is 
taken  off  across  the  brushes  A  and  B,  as  shown  in  a  and  more 
diagrammatically  in  b,  it  is  a  short  shunt.  If,  as  shown  in  c,  one 
end  of  the  shunt  be  taken  off  beyond  the  series  coil,  it  is  a  long  shunt. 
The  diagrams  b  and  c  indicate  the  reason  for  these  names.  So  far 


ELECTRO-MECHANICS.  447 

as  the  machine  itself  is  concerned,  there  is  but  little  difference 
between  long  and  short  shunt,  but,  as  will  be  shown  in  the  next 
chapter,  there  is  a  very  great  difference  in  the  three  classes  of 
machines  and  in  the  conditions  under  which  each  is  to  be  used. 

In  the  foregoing  diagrams  the  yoke  of  the  field  magnets  is 
represented  as  above  the  armature,  but  this  is  simply  for  clearness. 
While  they  may  have  any  position,  bipolar  machines  are  usually 
mounted  with  the  yoke  horizontal  and  below  the  armature,  or, 
less  frequently,  with  the  yoke  vertical  and  to  one  side. 

564.  Control  of  Field. — In  connection  with  this  subject,  refer- 
ence should  be  made  here  to  control  of  field.  Since  the  E.  M.  F. 
developed  in  a  generator  varies  with  the  rate  of  cutting  of  lines  of 
force,  if  the  field  be  constant,  the  E.  M.  F.  can  be  varied  only  by 
varying  the  speed  of  rotation.  Since,  however,  generators  are 

RHEOSTAT 


FIELD 
COIUS 


Fig.  276. 

usually  run  at  a  constant  speed,  the  E.  M.  F.  is  varied  by  increasing 
or  decreasing  the  number  of  lines  of  force,  that  is,  by  varying  the 
field.  In  a  shunt- wound  machine,  the  current  through  the  field 
coils,  and  consequently  the  field,  may  be  varied  by  means  of  a 
rheostat  in  series  in  the  shunt  circuit,  as  shown  in  Fig.  276.  In  a 


Fig.  277. 

series-wound  generator,  the  field  may  be  varied  by  a  rheostat  in 
parallel  with  the  field  coils  as  shown  in  Fig.  277.  The  greater  the 
current  through  the  rheostat,  the  less  through  the  field.  These 


448  ELEMENTS  OF  ELECTRICITY. 

field  rheostats  are  not  attached  to  the  generator  direct  but  are 
mounted  upon  a  switchboard,  an  auxiliary  piece  of  apparatus  which 
will  be  described  later  (Par.  579). 

565.  Armature  Core. — In  Par.  560  we  saw  that  the  enlarged 
portion  of  the  shaft  to  which  the  rotating  coils  are  attached  is 
called  the  armature  core.  This  core  has  two  separate  functions  to 
perform,  (a)  It  serves  as  a  rigid  base  of  attachment  for  these 
rotating  coils  and  is  therefore  cylindrical  in  shape,  (b)  As  ex- 
plained in  Par.  145  and  as  shown  in  Fig.  182,  it  diminishes  the  air 
gap  between  the  poles,  thereby  reducing  the  reluctance  in  the 
magnetic  circuit  and  increasing  the  flux.  It  must  therefore  be  of  a 
highly  permeable  material,  such  as  soft  iron.  It  not  only  increases 
the  flux  but  so  directs  it  that  the  lines  of  force  are  most  advan- 
tageously situated  for  being  cut  by  the  rotating  coils.  For  ex- 
ample, in  the  multipolar  machine  shown  in  cross-section  in  Fig. 
278,  if  the  armature  core  were  non-magnetic,  the  lines  of  force 


would  pass  directly  across  the  gaps  abed  and  therefore  would  not 
be  cut  by  the  coils,  but  this  core  being  of  iron,  the  lines  pass  into  it 
(Par.  145)  as  shown  in  the  diagram  and  are  cut  by  the  coils  as  they 
rotate. 

The  core  being  of  a  magnetic  substance  and  lying  between  the 
poles  of  the  field  magnets,  it  acquires  polarity  (Par.  119).  As  it 
rotates,  this  polarity  shifts  and  to  avoid  hysteretic  losses  (Par.  399) 
its  retentivity  should  be  very  small,  that  is,  it  should  be  made  of 
soft  and  pure  iron. 

Also,  since  it  is  a  conductor  rotating  in  a  magnetic  field,  eddy 
currents  will  be  produced  in  it,  and  to  reduce  these  it  is  laminated 
or  built  up  of  thin  sheets  (Par.  429). 

These  sheets  usually  take  the  form  of  punchings.  For  small 
machines  they  may  be  disc-shaped  and  perforated  with  a  single 


ELECTRO-MECHANICS. 


449 


hole  for  assembling  upon  the  shaft,  but  for  large  machines  they  are 
generally  segments  of  a  circle.  On  the  outer  periphery  they  are 
provided  with  slots  in  which  the  coils  are  wrapped  (Fig.  279)  and 
on  the  inner  there  are  undercut  grooves  by  which  they  are  as- 
sembled upon  a  spider  which  in  turn  is  keyed  to  the  shaft. 

ARMATURE     ..--LAMINATED  CORE 

— CQMMUTATOR 

SEGMENT 
INSULATION 


SHAFT 


-SPIDER 


K *»-••  DUCTS  FOR  VENTILATION 

Fig.  279. 


Although  this  lamination  diminishes  the  eddy  currents  it  does 
not  entirely  obviate  them  and  to  reduce  their  heating  effect  the 
core  is  not  built  up  solid  but  at  intervals  ventilating  spaces  are 
left.  The  air  currents  enter  between  the  spokes  of  the  spider  and 
emerge  through  these  ducts. 

566.  Classes  of  Armatures. — Based  upon  the  manner  in  which 
the  coils  are  wrapped  upon  the  core,  there  are  two  distinct  classes 
of  armatures,  the  ring  wound  and  the  drum  wound,  both  shown 
diagrammatically  in  Fig.  280.  Should  the  coil  after  passing 


RlNGj  WINDINq  DRUN  WINDING 

Fig.  280. 

through  a  slot  on  the  outer  surface  of  the  armature  be  threaded 
back  through  the  interior  of  the  core  (Fig.  279),  then  again  out 
through  a  slot  and  so  on,  in  other  words,  should  it  be  wrapped  in 
a  continuous  helix  around  the  rim  of  the  armature,  just  as  a  wire 
might  be  wrapped  around  the  rim  of  a  wagon  wheel  to  hold  a  tire 


450 


ELEMENTS  OF  ELECTRICITY. 


TERMINALS 


TERMINALS 


-VENTILATING  DUCT 


in  position,  it  is  a  ring  winding.  On  the  other  hand,  should  the 
coil,  after  passing  through  a  slot,  cross  along  a  chord  of  the  end 
of  the  core  and  return  by  a  slot  on  the  other  side,  it  is  a  drum 

winding. 

Electrically  the  two 
windings  do  not  differ 
in  principle  but  prac- 
tically the  drum  wind- 
ing is  used  almost  to 
the  exclusion  of  the 
ring  winding. 

One  objection  to  the 

Fig.  281.  .  -i.  .-I 

ring    winding  is  that 

the  conductor  of  which  the  coil  is  composed  must  be  put  on  by 
threading  it  back  and  forth  and  bending  it  into  place.  This  is 
difficult  with  the  large  copper  inductors  now  required;  moreover, 
any  insulation  about  the  coil  would  be  injured  in  this  process  so 
that  insulation  has  to  be 
put  on  as  the  coil  is 
placed  in  position,  and  it 
is  difficult  to  fasten  such 
coils  rigidly. 

On  the  other  hand,  the 
coils  for  a  drum  winding 
being  all  alike  may  be. 
made  up  on  a  form  and 
of  as  heavy  material  as 
may  be  desired  (Fig.  281). 
They  are  then  wrapped 
with  insulation,  baked  to 
expel  moisture  and  var- 
nished. Finally  they  are 
packed  tightly  into  the 
armature  slots  and  held 
securely  in  position  by 
wooden  wedges  inserted  as  shown  in  Fig.  282.  As  an  additional 
precaution,  a  certain  amount  of  banding  is  usually  wrapped  about 
the  armature. 

567.  The  Commutator.— In  Par.  556  we  saw  that  the  split  ring, 
or  arrangement  of  copper  segments  by  which  the  alternating  cur- 


Fig.  282. 


ELECTRO-MECHANICS. 


451 


rent  was  rectified,  is  called  the  commutator.  With  the  increase  in 
the  number  of  coils,  the  number  of  segments  also  increases  and 
they  finally  reduce  to  relatively  thin  wedge-shaped  copper  plates 
of  the  form  shown  in  Figs.  279  and  283.  In  the  upright  portion  or 
neck  of  these  segments  there  are  cut  mortises  into  which  the  coil 
terminals  are  soldered. 


,'COMMUTATOR   SEGMENT 
I 


RINGj 


Fig.  283. 


The  commutator  is  the  weakest  point  about  the  armature.  Not 
only  must  the  separate  segments  be  assembled  into  a  cylinder 
which  is  firmly  attached  to  the  armature  shaft  but  they  must  also 
be  perfectly  insulated  both  from  each  other  and  from  the  shaft. 
The  segments,  separated  by  sheets  of  mica,  are  arranged  in  a 
cylinder,  being  held  at  one  end  by  a  hub  or  sleeve  and  at  the  other 
end  by  a  wedge  ring,  from  both  of  which  they  are  insulated  by  a 
layer  of  a  composition  of  mica  and  shellac.  The  sleeve  and  the 
wedge  ring  are  drawn  tightly  together  by  means  of  bolts,  thus, 
binding  the  segments  rigidly  together,  and  these  are  then  turned 
down  to  a  perfect  cylinder. 

568.  Brushes. — The  brushes  are  so  named  because  in  the  earlier 
machines  they  were  of  brass  wire  and  resembled  a  stiff  paint 
brush.  In  the  process  of  evolution  these  took  the  form  (still  used 
in  certain  machines)  of  brass  laminae  like  the  leaves  of  a  book, 
then  were  made  of  copper  gauze  compressed  into  prisms.  They 
are  now  rectangular  blocks  of  carbon,  made  somewhat  in  the  same 
manner  as  the  carbons  for  arc  lights  (Par.  516)  except  that  there 
is  sometimes  incorporated  a  small  amount  of  paraffine  which  acts 
as  a  lubricant.  They  are  held  in  brush  holders  which  are  provided 
with  springs  by  which  the  pressure  of  the  brushes  against  the 


452 


ELEMENTS  OF  ELECTRICITY. 


commutator  may  be  regulated.  The  holders  in  turn  are  secured 
to  a  rocker  frame  by  which  the  brushes  may  be  shifted  bodily  in  the 
direction  of  rotation  of  the  commutator  or  in  contrary  direction. 
The  object  of  this  adjustment  is  explained  later  (Par.  570).  The 
brushes  must  be  proportioned  to  the  current  which  they  are  to 
carry  and  for  heavy  currents,  instead  of  being  of  a  single  large 
carbon  block,  each  consists  of  a  number  of  smaller  carbons  with 
separate  springs.  These  may  be  compared  to  the  finger  tips  of  a 
hand  pressing  lightly  upon  the  commutator.  Should  one  be 
momentarily  jarred  away  from  the  commutator,  the  others  pre- 
serve a  flexible  contact  and  the  circuit  is  not  broken.  It  will  be 
shown  later  (Pars.  573  and  577)  that,  except  for  one  class  of  drum 
windings,  there  are  required  as  many  brushes  as  there  are  poles. 

569.  The  Ring- Wound  Generator. — In  the  operation  of  a  gen- 
erator, the  current  flowing  through  the  coils  gives  rise  to  conditions 
which,  since  they  necessitate  certain  minor  corrections  and  ad- 
justments, should  be  thoroughly  understood.  On  account  of  the 


Fig.  284. 

greater  simplicity  of  the  diagram,  these  are  most  readily  explained 
by  reference  to  the  ring  winding,  but  it  must  be  remembered  that 
this  is  selected  merely  for  ease  of  explanation  and  that  the  majority 
of  modern  machines  are  drum  wound. 

Fig.  284  represents  diagrammatically  a  bipolar,  ring-wound 
generator.  In  this  diagram  the  extremities  of  each  turn  of  the 
winding  are  represented  as  connected  to  the  adjacent  commutator 
segments,  but  in  the  actual  machine  there  may  be  a  number  of 


ELECTRO-MECHANICS.  453 

turns  between  these  tapping  wires  (see  Fig.  286).  The  lines  of 
force  of  the  field,  as  shown  by  the  dotted  lines,  follow  around  the 
rim  of  the  armature  core  and  therefore  as  the  armature  rotates, 
only  the  outer  portion  of  the  coils  cuts  these  lines,  the  remaining 
portion  being  idle.  These  outer  portions,  the  inductors,  are  per- 
pendicular to  the  plane  of  the  paper  but,  in  order  that  they  may 
be  seen,  are  shown  as  part  of  the  helical  winding. 

Assuming  the  rotation  of  the  armature  to  be  clockwise,  applica- 
tion of  the  right  hand  rule  (Par.  422)  shows  that  the  direction  of 
the  induced  E.  M.  F.  in  each  inductor  to  the  right  of  the  sym- 
metrical plane  through  the  axis  of  the  armature  is  from  the  ob- 
server, while  that  hi  each  inductor  in  the  left  half  is  towards  the 
observer.  Beginning  at  the  bottom  inductor  on  either  side  and 
following  around  to  the  top,  the  instantaneous  value  of  the  E.  M.F. 
being  generated  in  each,  assuming  the  field  to  be  uniform,  is 
proportional  to  the  sine  of  the  angle  through  which  it  has  turned 
from  the  symmetrical  or  neutral  plane  (Par.  552),  and  these 
inductors  being  portions  of  a  continuous  helix,  the  total  E.  M.  F. 
in  each  half  of  the  armature  is  the  sum  of  these  separate  E.  M.  F.s. 
If,  therefore,  brushes  be  applied  at  A  and  at  B,  the  two  segments 
lying  in  the  neutral  plane,  and  be  connected  through  an  external 
circuit,  A  being  at  a  higher  potential  than  B,  a  current  will  flow 
out  by  A  and  returning  by  B  will  divide,  one-half  flowing  up  each 
side  of  the  armature  and  reuniting  at  A.  In  other  words,  the 
halves  are  in  parallel  and  afford  two  paths  for  the  current  through 
the  armature.  An  analogous  arrangement  would  be  the  grouping, 
shown  at  the  right  of  Fig.  284,  of  sixteen  cells,  two  in  parallel  and 
eight  in  series,  the  variation  in  the  E.  M.  F.  of  the  individual  cells 
being  indicated  by  the  length  of  the  lines  representing  the  cells. 

570.  Armature  Reaction. — The  tendency  of  the  field  magnets 
of  a  generator  is  to  magnetize  the  armature  core  by  induction. 
As  shown  in  Fig.  285,  a  north  pole  would  be  induced  at  N'  and  a 
south  pole  at  S'.  However,  when  the  generator  is  in  operation, 
each  half  of  the  ring  core  is  surrounded  by  many  ampere  turns  and 
is  therefore  powerfully  magnetized.  With  clockwise  rotation  the 
current  in  the  armature  alone  would  produce  a  north  pole  at  N" 
and  a  south  pole  at  S"  (Par.  404).  The  actual  magnetization  of 
the  ring  is  therefore  the  resultant  of  these  two,  and  a  north  pole 
will  be  found  at  some  intermediate  point  as  N"f  and  a  south  pole 
at  S'".  As  a  result  of  this  reaction  between  the  original  field  and 


454 


ELEMENTS  OF  ELECTRICITY. 


the  armature  field,  the  flux  will  be  distorted  as  shown  and  the 
neutral  plane  will  no  longer  coincide  with  the  symmetrical  plane 
but  will  be  shifted  forward  in  the  direction  of  rotation  to  some 
such  position  as  CC.  The  brushes  must  now  be  shifted  forward 
until  they  coincide  with  this  plane,  or  are  even  very  slightly  ahead 
of  it  (Par.  572).  This  adjustment  is  made  by  means  of  the  rocker 
frame  (Par.  568).  The  plane  in  which  the  brushes  are  finally 
placed  is  called  the  commutation  plane  and  the  angle  between  this 
and  the  symmetrical  plane  is  called  the  angle  of  lead. 


Fig.  285. 


The  advancing  of  the  brushes  and  variations  in  the  current 
through  the  armature  may  cause  further  shifting  of  the  plane  of 
commutation,  but  generators  are  now  so  constructed  that  when 
the  brushes  have  once  been  adjusted  and  the  machine  is  run  under 
average  conditions,  no  further  movement  is  needed. 

571.  Commutation. — Fig.  286  represents  diagrammatically  a 
portion  of  the  armature  of  a  ring-wound  generator  in  four  suc- 
cessive positions.  For  clearness  of  diagram,  the  brush  is  drawn 
below  the  commutator  segments.  The  broken  and  dotted  vertical 
line  represents  the  neutral  plane.  With  clockwise  rotation  and 
field  from  left  to  right,  currents  will  flow  through  the  coils  in  the 
direction  indicated  by  the  arrows. 

In  position  a,  the  brush  is  in  contact  with  segment  G  alone.  Of 
the  total  current  delivered  to  the  brush,  one-half  flows  in  from  the 
coil  C,  the  other  half  from  the  coil  B. 


ELECTRO-MECHANICS. 


455 


In  position  6,  the  armature  has  moved  until  the  brush,  still 
retaining  contact  with  G,  has  just  established  contact  with  F.  As 
before,  one-half  of  the  total  current  flows  in  from  C,  but  the  other 
half,  arriving  from  A,  divides  at  F,  a  small  but  rapidly  increasing 
portion  flowing  direct  to  the  brush,  the  diminishing  remainder 
flowing  through  B  to  G  and  thence  to  the  brush.  The  reason  why 
at  first  only  a  small  portion  flows  direct  from  F  to  the  brush  is 
that  F  is  then  in  contact  with  the  brush  along  a  narrow  strip  only 
and  the  resistance  of  this  contact  is  considerable.  However,  as 
the  armature  continues  to  move,  this  resistance  decreases  and  the 
current  through  F  increases,  that  through  B  decreasing  accord- 
ingly. 


Fig.  286. 


In  position  c,  the  brush  makes  equal  contact  with  F  and  G,  one- 
half  of  the  current  flows  through  CG,  the  other  half  through  AF, 
and  the  current  in  B  is  zero. 

In  position  d,  the  contact  with  F  has  increased  and  that  with  G 
has  dwindled  to  a  narrow  line.  At  this  instant,  the  full  current 
from  A  flows  through  F,  while  the  current  from  C,  for  reasons 
explained  above,  divides  at  G,  a  diminishing  portion  flowing 
through  G  direct  to  the  brush,  an  increasing  portion  flowing 
through  B  to  F. 

When  finally  the  brush  is  in  contact  with  F  alone,  the  conditions 
are  as  represented  in  a,  that  is,  one-half  of  the  total  current  flows 
from  A  to  F,  the  other  half  from  B  to  F.  Originally  the  current 
in  B  flowed  from  left  to  right  and  it  now  flows  from  right  to  left, 


456  ELEMENTS  OF  ELECTRICITY. 

in  other  words,  as  the  successive  segments  slip  past  the  brush,  the 
current  in  the  corresponding  coils  undergoes  complete  reversal. 

When  these  changes  of  the  current  in  the  coil  under  the  brush 
take  place  as  outlined  above,  the  commutation  is  said  to  be  perfect. 

572.  Sparking. — There  are  certain  conditions  which  interfere 
with  the  realization  of  perfect  commutation.     The  armature 
revolves  at  high  speed  and  the  reversal  of  the  current  in  a  coil 
often  takes  place  in  less  than  one-hundredth  of  a  second.    As 
these  coils  frequently  carry  from  fifty  to  one  hundred  amperes 
and  are  wrapped  about  an  iron  core,  the  self -induced  E.  M.  F.  is 
considerable.    The  effect  of  this  E.  M.  F.  is  to  oppose  any  change 
in  the  original  direction  of  the  current  flowing  in  the  coil,  therefore, 
in  position  d  in  Fig.  286  the  rise  of  the  current  from  G  into  B  is 
retarded  and  the  greater  part  of  the  current  from  C  is  forced  to 
flow  from  G  direct  into  the  brush.    As  the  area  of  contact  between 
the  brush  and  G  decreases,  the  current  density  (number  of  amperes 
per  square  centimeter  of  cross-section)  may  become  so  great  as  to 
produce  injurious  heating  of  the  brush  and  of  the  commutator 
segments.    Finally,  as  G  separates  from  the  brush,  a  momentary 
arc  is  produced,  its  heat  being  sufficient  to  volatilize  a  small 
portion  of  both  the  segment  and  the  brush.    Continuance  of  this 
"sparking"  will  injure  or  destroy  the  commutator. 

If  the  brush  be  moved  slightly  forward  in  the  direction  of 
rotation  of  the  armature  (as  for  example  under  coil  C  in  position 
d),  the  act  of  commutation  will  occur,  not  with  a  coil  which  is  in 
the  neutral  plane  but  with  one  in  which  there  is  being  induced  an 
E.  M.  F.  opposite  in  direction  to  the  self-induced  E.  M.  F.  This 
induced  E.  M.  F.  therefore  opposes  and  assists  in  overcoming  the 
self -induced  E.  M.  F.  and  removes  this  source  of  sparking.  Gen- 
erator brushes,  therefore,  are  usually  set  slightly  in  advance  of  the 
neutral  plane. 

573.  Multipolar    Generators. — Fig.    287    represents    diagram- 
matically  a  four-pole  ring-wound  generator.    Application  of  the 
right  hand  rule  shows  that  with  clockwise  rotation  the  direction 
of  the  induced  E.  M.  F.  is  as  represented  by  the  arrowheads.     If 
these  be  examined,  it  will  be  seen  that  the  E.  M.  F.  acts  from  the 
coils  to  the  commutator  in  two  points,  A  and  B,  and  from  the 
commutator  to  the  coils  in  two  other  points,  C  and  D.    Therefore, 
if  brushes  be  applied  at  these  four  points  and  be  connected  through 


ELECTRO-MECHANICS. 


457 


an  external  circuit,  currents  will  flow  out  from  A  and  B,  and 
return  by  C  and  D.  With  a  six-pole  machine  six  brushes  are 
needed  and  in  general  in  ring-wound  generators  as  many  brushes 
are  required  as  there  are  poles.  Brushes  of  like  polarity  are  usually 
connected  to  a  common  conductor,  a  ring,  to  which  in  turn  the 
corresponding  lead  is  attached. 

574.  Advantages  of  Multipolar  Machines. — Multipolar  ma- 
chines possess  some  important  advantages  over  bipolar  machines 
and  most  modern  machines  of  appreciable  power  are  of  this  type. 

(a)  When  a  coil  of  the  generator  represented  in  Fig.  287  has 
rotated  geometrically  through  180°,  it  has  rotated  electrically 


Fig.  287. 

through  360°.  With  a  six-pole  machine,  one-third  of  a  revolution 
carries  it  through  360°  electrically.  Therefore,  with  the  same 
number  of  lines  of  force  from  pole  to  pole,  the  same  E.  M.  F.  may 
be  developed  by  a  four-pole  machine  with  an  angular  velocity 
only  half  as  great  as  that  of  the  bipolar  machine.  Or,  if  the 
angular  velocity  of  the  two  be  the  same,  the  multipolar  machine 
will  develop  the  greater  E.  M.  F. 


458 


ELEMENTS  OF  ELECTRICITY. 


(b)  Examination  of  the  figure  will  show  that  the  current  coming 
in  to  the  machine  divides  equally  between  C  and  D  and  from  each 
of  these  points  has  two  paths  to  the  positive  brushes  A  and  B,  in 
other  words,  the  current  through  the  armature  has  as  many  paths 
in  parallel  as  the  machine  has  poles.  With  the  same  sized  in- 
ductors, the  resistance  through  the  armature  of  a  four-pole 
machine  is  only  one-half  of  that  of  a  bipolar  machine,  or,  with  the 
same  total  current,  the  inductors  of  the  four-pole  machine  carry 
only  one-half  the  current  as  those  of  the  bipolar.  This  is  of  great 
importance  in  generators  handling  large  currents. 

Minor  advantages  of  the  multipolar  machines  are  the  more 
advantageous  distribution  of  the  flux  and  the  less  weight  of  iron 
required  in  the  field  magnets. 

575.  Drum  Windings. — The  distinguishing  feature  of  the  drum 
winding  has  already  been  given  (Par.  566).  Since  the  coils  are 
arranged  with  the  inductors  at  opposite  ends  of  a  chord  of  the 
armature  core  (Fig.  280),  if  the  induced  E.  M.  F.  in  one  of  these 
inductors  acts  from  front  to  rear,  that  in  the  other  must  act  from 
rear  to  front.  Hence,  the  principle  governing  all  drum  windings 
is  that  the  coils  must  be  so  wrapped  that  the  two  inductors  are 
never  simultaneously  under  like  poles.  There  are  a  number  of 
different  windings  which  fulfill  this  condition  but  they  all  belong 
to  one  or  the  other  of  two  general  classes,  wave  winding  and  lap 
These  will  be  explained  below. 


576.  Plane  Development  of  Drum  Winding. — There  are  two 
conventional  ways  of  representing  diagrammatically  a  drum 
winding.  The  first  is  to  develop  the  armature  by  placing  it 


LAP  WINDING 


Fig.  288. 


WAVE 


on  its  side  and  rolling  it  along  on  a  plane.  Fig.  288  represents 
in  simplest  form  such  a  development  of  a  lap  winding  and  of  a 
wave  winding  (both  incomplete),  and  indicates  the  appropriate- 
ness of  these  names. 


ELECTRO-MECHANICS. 


459 


N 

i 
i 

s 

i 

i 

N 

I 

i 
i 

5 

Fig.  289  represents  a  lap  winding  for  a  four-pole  generator,  the 
armature  carrying  sixteen  inductors  and  eight  commutator  seg- 
ments. The  coils  are  composed  of  inductors  1  and  6,  3  and  8,  5  and 
10,  etc.  It  will  be  noted  that  in  each  the  two  inductors  are  under 
different  poles.  Furthermore,  if  we  begin  at  inductor  No.  1  and 
follow  the  winding  through,  it  will  be  seen  that  we  pass  in  succes- 
sion through  all  of  the  inductors  and  finally  return  to  the  starting 
point;  in  other  words,  just  as  in  the  ring  winding,  the  inductors  are 
in  series  and  the  winding  is  a  closed  coil  (Par.  559). 


IN!  POLES 


INDUCTORS 


!  COMMUTATOR  BARS 
BRUSHES 


With  rotation  from  left  to  right,  the  direction  of  the  induced 
E.  M.  F.  is  as  indicated  by  the  arrowheads,  and  by  inspection  the 
position  of  the  positive  brushes  is  readily  located  at  segments 
3  and  7  and  that  of  the  negative  brushes  at  segments  1  and  5. 

577.  Star  Development  of  Drum  Winding. — An  objection  to  the 
foregoing  diagram  is  that  the  windings  are  not  represented  as  clos- 
ing upon  themselves.  To  remedy  this,  use  is  made  of  what  may 
be  termed  a  star  development.  If  we  should  stand  a  barrel  on  end, 
cut  all  of  the  hoops  except  the  one  at  the  top,  open  out  the  staves 
from  the  bottom  until  the  head  rested  upon  the  ground  with  the 
staves  radiating  like  the  petals  of  a  daisy,  we  should  have  a  star 
development  of  the  barrel.  Applying  this  to  an  armature,  the 
commutator  corresponds  to  the  head  of  the  barrel  and  the  inductors 
to  the  barrel  staves.  The  inductors  and  their  connections  are 
thus  shown  in  their  proper  relation  to  the  commutator  segments 
and  the  windings  close,  the  only  distortion  occurring  in  the  cross 
connections  at  the  back  end  of  the  armature.  Such  a  projection 


460 


ELEMENTS  OF  ELECTRICITY. 


of  a  lap  winding  for  a  four-pole  machine  is  given  in  Fig.  290.  The 
heavy  radial  lines  represent  the  inductors.  To  enable  the  eye  to 
trace  the  back  connections  with  least  difficulty,  these  latter  are 
drawn  in  a  regular  geometric  pattern  with  salient  angles. 

With  clockwise  rotation,  the  direction  of  the  induced  E.  M.  F. 
is  as  indicated  by  the  arrowheads.  If  the  circuits  be  traced,  it  will 
be  seen  that  there  should  be  four  brushes  and  that  they  should  be 
located  as  indicated  in  the  diagram.  There  are,  therefore,  four 


Fig.  290. 

paths  through  the  armature.  For  this  reason,  the  lap  winding  is 
frequently  spoken  of  as  a  parallel  winding.  It  is  best  suited  for 
the  production  of  large  currents  at  low  voltage. 

A  star  projection  of  a  wave  winding  for  a  four-pole  machine  is 
shown  in  Fig.  291.  In  addition  to  the  manner  in  which  it  is  put 
on,  this  winding  differs  from  the  lap  winding  in  several  other 
respects,  particularly  in  requiring  but  one  pair  of  brushes.  The 
positions  of  the  positive  and  the  negative  brushes  are  shown  in  the 


ELECTRO-MECHANICS. 


461 


diagram.  Should  an  additional  negative  brush  be  introduced  at  ic 
and  connected  to  6,  it  would  be  of  na  appreciable  electrical  effect, 
for  examination  of  the  diagram  will  show  that  c  and  b  are  already 
connected  through  the  coil  cdeb  in  which,  at  the  instant  shown, 
no  E.  M.  F.  is  being  induced.  The  inductors  of  a  wave  winding 
are  therefore  in  series  and  there  are  but  two  paths  through  the 
armature,  for  which  reasons  wave-wound  armatures  are  best 
suited  for  the  production  of  small  currents  of  high  voltage. 


Fig.  291. 

578.  Calculation  of  E.  M.  F.  of  Generator. — The  E.  M.  F.  of  a 

generator  may  be  calculated  as  follows: 

Let  <£=flux  from  each  pole 
n  =  number  of  poles 
n'  =  number  of  revolutions  per  second 
n" = number  of  paths  through  the  armature 
N= number  of  inductors   - 


462  ELEMENTS  OF  ELECTRICITY. 

'  The  number  of  flux  lines  cut  by  each  inductor  in  one  revolution 
is  n.<£. 

The  number  of  flux  lines  cut  by  each  inductor  per  second  is 
n'.n.Q. 

The  E.  M.  F.  generated  by  each  inductor  is  nf.  n .  <£/108. 

But  since  there  are  N/n"  inductors  in  series,  the  total  E.  M.  F. 
.  N .  nf .  n .  <f>  ,, 

*    «".io»    volts- 

579.  Switchboards. — A  generator  may  be  called  upon  to  furnish 
current  for  various  uses,  as,  for  example,  for  lighting,  for  charg- 
ing a  storage  battery,  for  running  a  motor,  etc.,  etc.,  and  it  may 
be  required  to  do  these  things  one  at  a  time  or  in  various  com- 
binations. Wires  must  therefore  be  run  from  the  generator  to 
the  lamps,  battery,  machines,  etc.,  and  there  must  be  switches 
in  the  various  circuits.  The  generator  must  be  supplied  with 
a  field  rheostat  (Par.  564)  by  which  its  E.  M.  F.  may  be  adjusted, 
and  this  implies  that  it  must  also  be  equipped  with  a  voltmeter 
by  which  this  E.  M.  F.  may  be  measured.  If  a  storage  battery 
is  to  be  charged,  its  E.  M.  F.  must  be  known  before  the  current 
from  the  generator  can  be  turned  on  (Par.  245).  It  is  also  often 
desirable  to  know  the  current  flowing  in  any  one  of  the  circuits, 
and  for  this  there  must  be  ammeters.  Overload  switches  should 
be  inserted  in  the  principal  circuits  and  an  underload  switch 
must  be  in  the  charging  circuit  for  the  storage  battery  (Par. 
415).  Should  an  attempt  be  made  to  connect  these  various 
switches  and  instruments  to  the  generator  direct,  the  machine 
would  be  hidden  in  a  hopeless  maze  of  wiring.  These  auxiliary 
pieces  of  apparatus  are  therefore  gathered  together,  taken  to 
one  side  and  mounted  upon  a  switchboard.  Wires  from  the 
machine,  not  exceeding  three  in  number,  are  brought  over  in  a 
conduit  and  the  distribution  of  electrical  energy  takes  place  at 
the  board.  This  distribution  is  usually  made  from  two  heavy, 
parallel  copper  bars,  called  bus  bars,  which  are  connected  to  the 
source  of  the  electrical  energy  and  which  may  be  regarded  as  its 
enlarged  terminals. 

Originally  of  minor  consideration,  the  switchboard  has  now 
risen  to  a  position  of  importance  second  only  to  that  of  the 
machine  itself  and  frequently  rivalling  it  in  cost.  It  is  composed 
of  panels  of  some  non-conducting  material,  preferably  marble, 
upon  the  front  of  which  are  mounted  the  switches  and  instru- 


ELECTRO-MECHANICS. 


463 


ments;  the  bus  bars,  wiring  and  connections  being  at  the  back.  In 
addition  to  a  symmetrical  distribution  of  the  apparatus,  it  is  cus- 
tomary to  arrange  parallel  wires  of  a  circuit  on  direct-current 
switchboards  so  that  if  they  be  horizontal,  the  upper  one  is  the 
positive  wire;  if  they  be  vertical,  the  right  hand  one  is  positive. 


LAMPS 


STORAGE   BATTERS  GENERATOR 

Fig.  292. 

In  drawings  of  switchboards,  several  conventions  are  observed. 
Wires  are  always  drawn  as  right  lines  which  are  perpendicular 
or  parallel  to  the  lower  edge  of  the  board  (Fig.  292).  This  is  to 
aid  the  eye  in  tracing  the  circuits.  If  two  wires  cross  but  are  not 
connected  electrically,  this  fact  may  be  indicated  by  a  little  arch 
in  one  of  the  wires,  or  they  may  be  assumed  not  to  make  connec- 
tion unless  a  dot  be  made  upon  the  point  of  intersection. 


464  ELEMENTS  OF  ELECTRICITY. 

580.  Example  of  Switchboard. — A  switchboard  by  which  the 
current  from  a  shunt-wound  generator  may  be  used  to  run  a 
number  of  lamps  and  charge  a  storage  battery,  either  separately 
or  simultaneously,  is  shown  in  Fig.  292.    The  circuits  are  easily 
followed  by  the  eye  and  the  use  of  the  various  switches  will  be 
understood  from  the  following: 

To  charge  the  battery: 

(a)  Close  b  to  the  left  and  read  the  battery  voltage. 
(&)  Start  the  generator.     Close  b  to  the  right  and  read  the 
generator  voltage.     Manipulate  the  field  rheostat  until 
the  generator  voltage  is  about  ten  per  cent  greater  than 
the  battery  voltage. 

(c)  Close  a,  c,  and  last  the  underload  switch. 
To  run  the  lights  at  the  same  time: 

Close  also  d. 
To  run  the  lights  separately: 

With  the  above  arrangement  open  c. 

(It  will  be  noted  that  the  lights  are  now  run  through  the  under- 
load switch.  This  is  not  correct.  An  additional  switch  should 
be  used  by  which  the  generator  may  be  thrown  direct  on  the  bus 
bars.  It  is  omitted  in  the  diagram  to  avoid  overcrowding  the 
figure.) 

The  right  hand  ammeter  reads  the  current  from  the  generator. 
To  run  the  lights  from  the  battery  alone: 

With  all  switches  open,  close  c  and  d. 
The  left  hand  ammeter  now  reads  the  current  from  the  battery. 

581.  Coupling  of  Generators;    Three- Wire  System. — In  Par. 
502  it  was  shown  that  the  successful  transmission  of  electrical 
power  to  a  distance  depended  upon  the  employment  of  high 
voltage,  the  loss  of  power  in  the  leads  varying  inversely  as  the 
square  of  this  voltage.    Alternating  currents  are  easily  stepped 
up  for  transmission  and  as  easily  stepped  down  at  the  point 
where  they  are  to  be  utilized.    In  the  case  of  direct  currents  the 
transformation  is  much  more  troublesome  and  expensive.     For 
such  currents,  however,  there  has  been  devised  a  system  by 
which  the  voltage  may  be  doubled  and  thus  the  advantage  of 
high  voltage  transmission  be  partly  secured.    This  will  be  under- 
stood from  the  following  explanation.     It  is  desired  to  operate 
at  a  distance  a  number  of  110  volt  incandescent  lamps.     If  two 


ELECTRO-MECHANICS.  465 

generators,  A  and  B,  each  capable  of  delivering  110  volts  to  the 
lamps,  be  connected  in  series  as  shown  in  Fig.  293,  the  voltage 
between  the  leads  will  be  220.  If  the  lamps  between  C  and  D 
be  arranged  two  in  series,  each  will  receive  its  required  110  volts, 


rat 


Fig.  293. 

while  the  currents  in  the  leads  will  be  only  one-half  of  that  re- 
quired by  the  same  number  of  lamps  arranged  singly  in  parallel. 
The  leads  therefore  may  be  reduced  three-quarters  in  size.  If  now 
a  third  wire  NN,  the  neutral,  be  inserted  as  shown  in  the  figure, 
it  will  be  possible  to  have  a  different  number  of  lamps  on  the 
two  sides.  If  there  be  more  lamps  above  the  neutral  than  below, 
the  excess  current  flows  in  on  the  neutral;  if  there  be  less  above, 
the  excess  current  flows  out  on  the  neutral,  in  other  words,  the 
neutral  needs  only  be  sufficiently  large  to  carry  the  difference  in 
the  currents  required  on  the  two  sides.  In  practice,  however, 
it  is  made  of  the  same  size  as  the  other  two  leads.  Notwithstand- 
ing the  extra  wire,  the  saving  in  copper  in  this  three-wire  system 
is  five-eighths,  or  62.5  per  cent,  of  the  amount  required  in  a  two- 
wire  system  for  transmitting  equal  power.  Against  this  saving 
must  be  put  the  cost  of  the  extra  generator  (though  certain  special 
generators  have  been  devised  to  supply  a  three-wire  system 
from  a  single  machine),  and  the  extra  cost  of  installation  and  of 
switches  and  switchboard  appliances,  so  that  frequently  the 
saving  is  more  apparent  than  real.  In  addition  to  this,  more 
attention  is  required  in  regulating  the  two  generators  since  with 
unequal  loads  on  the  two  sides  of  the  neutral,  the  E.  M.  F.  of 
the  generators  must  differ. 

The  principle  involved  has  been  applied  abroad  to  a  five-wire 
system. 


466  ELEMENTS  OF  ELECTRICITY 


CHAPTER  41. 

GENERATOR   CHARACTERISTICS. 

582.  Adaptation  of  Generator  to  Work  Required.— Of  the  vari- 
ous proposed  classifications  of  direct  current  generators,  the 
most  important  is  the  one  based  upon  the  excitation  of  the  field 
magnets  (Par.  563),  that  is,  into  series,  shunt  and  compound 
machines. 

Each  one  of  these  classes  possesses  certain  advantages  and 
disadvantages  which  render  it  more  suitable  for  some  purposes 
and  less  so  for  others. 

As  an  illustration,  suppose  we  have  at  our  disposal  a  series 
generator  and  a  shunt  generator  and  are  required  to  charge  a 
storage  battery:  which  of  the  two  should  we  use? 

To  prevent  the  storage  battery  from  discharging  back  through 
the  generator,  the  voltage  of  the  latter  must  be  kept  constantly 
higher  than  that  of  the  battery.  Suppose  we  were  to  start  with 
the  series  generator.  Its  E.  M.  F.  can  not  build  up  until  a 
current  flows  through  the  field  coils,  and  no  current  can  flow 
through  these  until  the  external  circuit  is  completed.  There- 
fore, should  we  simply  start  the  generator  and  then  switch  it 
on  to  the  storage  battery,  the  battery  would  discharge  back 
through  the  generator.  We  must  then  first  build  up  its  field 
by  sending  the  current  through  some  external  circuit  other  than 
that  which  includes  the  battery  and  then,  when  the  E.  M.  F. 
has  reached  the  proper  point,  switch  the  current  in  on  the 
battery. 

Suppose  this  to  have  been  done  and  that  the  connections  are 
as  shown  diagrammatically  in  Fig.  294.  As  the  battery  becomes 
charged,  its  voltage  rises,  consequently  the  current  sent  through 
it  by  the  generator  grows  smaller.  The  current  through  AB 
being  smaller,  the  field  gets  weaker:  the  voltage  of  the  generator 
consequently  falls;  this  again  causes  the  current  to  decrease; 
the  field  gets  still  weaker,  and  so  on.  In  other  words,  the  generator 
unbuilds  and  "drops  its  load,"  and,  unless  there  be  an  under- 
load switch  in  the  circuit,  the  battery  will  soon  discharge  back. 


ELECTRO-MECHANICS.  467 

A  series-wound  generator  is  therefore  not  fitted  to  charge  a  stor- 
age battery. 


P 


FIELD  BATTERY 


Fig.  294. 

On  the  other  hand,  suppose  that  we  employ  the  shunt  generator 
and  that  it  is  connected  as  shown  in  Fig.  295.  The  generator  is 
started  and,  the  current  flowing  through  the  shunt  field  A  B, 
the  E.  M.  F.  builds  up  rapidly.  When  the  voltage  has  reached 
the  proper  point,  the  switch  S  is  closed  and  the  current  is  thrown 
in  on  the  battery.  As  the  battery  becomes  charged,  its  voltage 
rises  and  this  counter  E.  M.  F.  cuts  down  the  current  from  the 
generator  but  the  effect  is  very  different  from  that  in  the  case 
of  the  series  generator.  As  the  current  from  the  shunt  generator 
decreases,  its  voltage  increases.  The  explanation  of  this  is  as 
follows.  The  E.  M.  F.  of  the  generator  at  any  instant  is  spent 


Fig.  295. 

in  doing  two  things,  driving  the  current  through  the  resistance 
of  the  armature  coils  and  brush  contacts  (or  through  the  internal 
resistance  of  the  machine),  and  driving  it  through  the  resistance 
of  the  external  circuit,  including  the  overcoming  of  any  counter 
E.  JVE.  F.  in  that  circuit.  This  will  be  recognized  as  but  another 
example  of  lost  and  useful  volts  as  discussed  in  Par.  305.  The 
smaller  the  current  through  the  armature,  the  smaller  the  lost 
volts,  or  the  internal  drop  Ir,  and  the  more  nearly  the  voltage 
between  A  and  B  approaches  the  E.  M.  F.  of  the  generator. 
We  see  then  that  the  voltage  of  the  shunt  generator  always  re- 
mains greater  than  that  of  the  battery  and  that  the  charging  can 
be  done  with  safety. 


468 


ELEMENTS  OF  ELECTRICITY. 


583.  Characteristics. — The  advantages  and  disadvantages  of 
the  various  forms  of  generators  may  be  discussed  in  a  similar 
manner  to  the  foregoing.    Where  constancy  of  current  is  to  be 
maintained,  a  series  generator  is  under  certain  conditions  satis- 
factory;  where  constancy  of  voltage  is  desired,  a  shunt  or  a 
compound  generator  must  be  employed.      However,  we  might 
sometimes  overlook  some  point  in  our  discussion  or  might  give 
undue  weight  to  some  other,  therefore,  the  most  sure  method 
is  actually  to  try  the  machine  under  varied  conditions,  keep  a 
record  of  the  results,  tabulate  and  compare  these.     If  they  can 
be  put  graphically  in  the  form  of  a  curve,  they  give  a  clearer 
conception  of  the  working  of  the  machine.    Such  curves  are  called 
"characteristics"  and  much  information  can  be  derived  from  their 
study. 

584.  Magnetization  Characteristics. — As  an  illustration  of  these 
characteristics,  suppose  that  we  have  a  generator  whose  field  is 


AMPERES 


Fig.  296. 


excited  from  a  separate  source,  such  as  a  storage  battery.  We 
rotate  the  generator  at  a  constant  speed,  we  excite  the  field  by 
various  currents  and  we  record  the  strength  of  the  exciting  cur- 
rent and  the  corresponding  voltage  across  the  brushes  of  the 
generator.  Plotting  this  data  with  amperes  as  abscissae  and  the 
corresponding  volts  as  ordinates,  we  obtain  a  curve  (Fig.  296) 
which  is  called  the  "magnetization  characteristic" 

A  study  of  this  reveals  (a)  that  with  no  current  in  the  field 
coils  there  is  still  a  small  voltage,  OA,  due  to  the  residual  magnet- 
ism of  the  magnet  cores  (Par.  562),  and  (b)  that  as  the  amperes 
in  the  field  coils  increase  regularly,  the  voltage  at  first  rises  rapidly 


ELECTRO-MECHANICS. 


469' 


and  then  more  slowly.  Reflection  will  show  that  this  curve  is 
nothing  more  than  the  magnetization  curve  described  and  figured 
in  Par.  393. 

585.  Characteristic  of  Series  Generator. — Fig.  297  represents 
diagrammatically  a  series  generator  run  at  constant  speed  and 

FIELD 


AMMETER 
Fig.  297. 

connected  in  circuit  with  a  number  of  lamps  in  parallel  and  an 
ammeter.  A  voltmeter  is  connected  across  the  brushes.  By 
turning  on  lamps  the  resistance  of  the  circuit  is  reduced  and  the 
current  thereby  increased.  This  current  is  measured  by  the  am- 
meter  and  the  corresponding  terminal  voltage  is  given  by  the 
voltmeter.  If  the  amperes  be  laid  off  as  abscissae  and  the  cor- 
responding volts  as  ordinates,  the  resulting  curve,  ABMN,  Fig. 
298,  is  the  external  characteristic,  so  called  because,  as  was  pointed 


D       AMPERES 
Fig.  298. 

out  above  (Pars.  461  and  582),  the  voltage  read  by  the  voltmeter 
is  not  the  total  E.  M.  F.  of  the  machine  but  only  the  IR  drop 
over  the  external  circuit,  in  other  words,  the  useful  volts.  Should 
we  wish  to  represent  the  total  E.  M.  F.,  the  internal  drop,  or 
lost  volts  7r,  must  be  added  to  the  external  drop. 


470  ELEMENTS  OF  ELECTRICITY. 

Since  r,  the  internal  resistance  of  the  machine,  is  constant, 
the  internal  drop  varies  directly  as  the  current  and  is  represented 
in  Fig.  298  by  the  straight  line  OF.  If  the  ordinates  of  OF  be 
added  to  the  corresponding  ordinates  of  the  curve  ABMN,  the 
resulting  curve  OH  is  the  total  E.  M.  F.  curve  or  the  internal 
characteristic.  Were  it  not  for  the  effects  of  armature  reaction, 
this  curve  would  agree  with  the  magnetization  curve  described 
in  the  preceding  paragraph. 

Examination  of  the  external  characteristic  shows  that  the 
machine  should  be  operated  with  currents  corresponding  to  the 
flatter  portion  of  the  curve,  for  if  the  current  falls  below  KO, 
slight  changes  in  the  current  produce  great  fluctuations  in  the 
voltage  and  the  operation  of  the  machine  is  unstable. 

'  .586.  Critical  Resistance.— From  the  figure,  MD/DO  is  the 
tangent  of  the  angle  MOD,  and  since  MD  represents  E.  M.  F. 
and  OD  represents  current,  E/I  =  tan  0.  But  from  Ohm's  law 
E/I  =  R,  hence,  at  any  point  upon  the  external  characteristic 
the  corresponding  external  resistance  is  proportional  to  the  tan- 
gent of  the  angle  which  the  ordinate  at  that  point  subtends. 

As  the  external  resistance  is  increased,  the  angle  6  increases 
and  the  point  M  moves  towards  B.  Finally,  a  very  slight  in- 
crease in  6  will  cause  M  to  drop  to  the  origin.  There  is  therefore 
for  a  series  generator  an  external  resistance,  the  critical  resistance, 
beyond  which  the  generator  will  not  operate.  Reflection  will 
show  the  correctness  of  this  conclusion  since  the  resistance  must 
always  be  small  enough  to  permit  a  sufficient  current  to  flow 
through  the  field  coils  and  produce  the  necessary  strength  of  field. 

587.  Characteristic  of  Shunt  Generator. — If  a  shunt  gener- 
ator be  connected  up  as  shown  in  Fig.  299  and  data  be  obtained 


AMMETER  N 


Fig.  299. 

and  characteristic  plotted  as  described  in  Par.  585,  the  resulting 
curve  (Fig.  300)  will  be  seen  to  differ  widely  from  the  one  obtained 
from  the  series  machine.  To  begin  with,  the  voltage  is  a  maximum 


ELECTRO-MECHANICS. 


471 


when  there  is  no  current  in  the  external  circuit.  As  the  current 
is  increased,  the  voltage  falls  quite  regularly  until  a  final  point  is 
reached  when  a  further  decrease  in  the  external  resistance  causes 
both  the  current  and  the  voltage  to  drop  and  if  all  resistance  be 
removed,  the  machine  unbuilds  entirely  and  the  curve  returns 
upon  the  origin. 


Fig.  300. 

The  foregoing  results  are  brought  about  by  two  causes.  First, 
the  current  through  the  shunt  grows  smaller  and  the  field  con- 
sequently weaker.  Whatever  decreases  the  difference  of  potential 
between  A  and  B  (Fig.  299)  decreases  the  current  through  the 
field  coils.  With  no  current  in  the  external  circuit,  the  full  E.  M. 
F.  of  the  machine  is  available  for  driving  current  through  the 
shunt.  When,  however,  a  current  flows  through  the  armature, 
the  available  E.  M.  F.  is  the  total  E.  M.  F.  diminished  by  the 
internal  drop,  7r,  which  last  varies  directly  with  the  current. 
At  first,  as  the  field  current  weakens,  the  voltage  is  not  greatly 
affected  since  the  field  magnets  are  being  worked  on  the  upper 
part  of  the  magnetization  curve.  When,  however,  the  magnet- 
ization falls  below  the  bend  of  the  curve,  it  drops  rapidly  as  the 
exciting  current  decreases. 

Second,  the  field  is  weakened  by  the  armature  reaction.  Con- 
sider the  diagram  (Fig.  301)  of  the  drum- wound  bipolar  machine. 
With  clockwise  rotation,  the  brushes  will  be  shifted  from  the 
symmetrical  plane  to  the  positions  A  and  D  (Par.  570).  In  the 
inductors  in  the  semi-circumference  A  BCD,  the  current  is  flowing 


472 


ELEMENTS  OF  ELECTRICITY. 


in;  in  the  other  semi-circumference  it  is  flowing  out.  The  effect 
of  the  current  in  the  inductors  C  to  D  and  A  to  F  is  to  produce  a 
field  in  the  direction  of  the  large  arrow,  that  is,  opposite  to  the 
field  of  the  magnets  and  consequently  weakening  that  field,  and 
this  effect  increases  as  the  current  through  the  armature  increases. 


Fig.  301. 

For  this  reason,  the  ampere  turns  between  C  and  D  and  between 
A  and  F,  or  in  the  double  angle  of  lead,  are  named  the  demagnet- 
izing turns. 

The  critical  resistance  for  a  shunt  generator  is  that  resistance 
of  the  external  circuit  which  if  reduced  will  cause  the  machine 
to  unbuild. 

588.  Compound  Generator. — The  properties  desired  of  a  gener- 
ator vary  in  accordance  with  the  use  to  which  the  current  is  to 
be  put.    In  some  circumstances  constancy  of  current  is  required; 
in  others,  constancy  of  potential.    Of  these,  the  more  important, 
notably  in  the  case  of  electric  lighting  (Par.  511),  is  constancy  of 
potential.    Neither  the  series  nor  the  shunt  generator  afford  this 
desired  constancy.     However,  we  have  shown  above  that  the 
voltage  of  a  series  generator  rises  as  the  current  is  increased, 
while  that  of  the  shunt  machine  falls  with  this  increase.    The 

,  logical  attempt  to  combine  these  windings  in  one  machine  so  that 
their  effects  counterbalance,  has  led  to  the  development  of  the 
compound  generator.  This  compounding  may  be  so  carried  out 
that  the  voltage,  even  under  wide  fluctuations  in  the  current, 
remains  nearly  constant. 

589.  Overcompounding. — If  in  a  compound  machine  the  series 
coils  be  given  a  few  more  turns  than  are  needed  to  preserve  con- 
stant potential,  the  voltage  rises  with  increase  of  current,  although 


ELECTRO-MECHANICS.  473 

not  so  rapidly  as  in  the  case  of  the  simple  series  machine.  The 
generator  is  then  said  to  be  over  compounded.  The  object  of  over- 
compounding  will  be  understood  from  the  following.  Let  G,  Fig. 
302,  represent  a  compound  generator  supplying  current  to  a  dis- 

l  OHM  c 


B  1  OHM 

Fig.  302. 

tant  group  of  lamps  CD.  Suppose  each  lamp  to  require  one 
ampere  at  100  volts  and  suppose  the  resistance  of  the  leads  AC 
and  BD  to  be  each  one  ohm.  When  one  lamp  is  turned  on,  there 
is  a  drop  of  one  volt  from  A  to  C,  and  of  one  volt  from  D  to  B. 
In  order  therefore  that  the  voltage  between  C  and  D  shall  be  100, 
the  generator  must  develop  between  its  brushes  102  volts.  If  all 
five  lamps  be  turned  on,  there  will  be  a  drop  of  five  volts  from 
A  to  C,  and  of  five  from  D  to  B;  the  generator  must  therefore 
develop  between  its  brushes  110  volts.  We  see  then  that  a  gener- 
ator is  overcompounded  so  that  a  constant  difference  of  potential 
may  be  maintained  between  two  points  at  a  distance  from  the 
generator. 


474  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  42. 

DIRECT  CURRENT  MOTORS. 

590.  The  Motor  and  the  Generator  Identical. — An  electric 
generator,  as  we  have  already  seen,  is  a  machine  to  which 
mechanical  energy  is  applied  and  from  which  electrical  energy 
is  drawn;  on  the  other  hand,  an  electric  motor  is  a  machine  to 
which  electrical  energy  is  applied  and  from  which  mechanical 
energy  is  derived.  Electrically,  they  are  identical,  and  a  machine 
which  if  turned  by  mechanical  power  will  produce  a  current, 
will,  if  supplied  with  a  current,  develop  mechanical  power.  The 
truth  of  this  statement  may  be  shown  by  the  following  simple 
illustration.  Fig.  303  represents  the  arrangement,  already  de- 


I         I       I      "A 

Fig.  303. 

scribed  several  times,  of  a  wire  sliding  on  parallel  conducting 
rails  which  include  between  them  a  magnetic  field.  The  wire  AB 
is  a  conductor  in  a  magnetic  field  and  if  pushed  in  the  direc- 
tion C,  there  will  be  induced  in  it  a  current  from  A  to  B  (Par. 
422);  it  is  therefore  a  generator  in  its  simplest  form.  If  instead 
of  pushing  the  wire,  a  current  be  passed  through  it  from  A  to  B, 
it  becomes  a  conductor  carrying  a  current  and  placed  in  a  magnetic 
field  and  experiences  a  force  (Par.  356)  which  will  cause  it  to 
move  in  the  direction  D  (Par.  352);  it  is  therefore  also  a  motor. 

591.  Explanation  of  Motion.— Let  AB,  Fig.  304,  represent  a 
coil  of  wire  placed  in  a  magnetic  field  NS  and  free  to  revolve 
about  the  axis  CD.  If  a  current  be  sent  through  this  coil  it  will 
start  to  rotate.  The  simplest  explanation  of  this  motion  is  that 
each  side  of  the  coil  is  a  conductor  carrying  a  current  and  placed 


ELECTRO-MECHANICS. 


475 


in  a  magnetic  field  and  is  therefore  acted  upon  by  a  force  which 
is  at  right  angles  to  the  field  and  whose  strength  is  (Par.  356) 

/=/.  H.I  dynes 

In  this  expression  I  is  the  current  in  absolute  units,  H  is  the 
strength  of  the  field,  or  number  of  lines  of  force  per  square  centi- 
meter, and  I  is  the  length  in  centimeters  of  the  wire  at  right  angles 


Fig.  304. 


to  the  field.  The  direction  of  the  current  in  one  side  of  the  coil 
being  opposite  to  that  in  the  other,  the  force  acting  upon  one  side 
is  opposite  to  that  acting  upon  the  other;  in  other  words,  the  two 
forces  constitute  a  couple  and  rotation  will  be  produced.  Its 
direction  may  be  determined  by  applying  the  left  hand  rule  (Par. 
352). 

The  following  additional  explanation  of  this  movement  is  given 
as  it  involves  certain  conceptions  which  will  be  used  in  a  discus- 
sion later  on. 

The  lines  of  force  of  the  field  run  from  N  to  S  as  shown  by  the 
heavy  arrow.  If  a  current  enters  the  coil  by  A  and  leaves  by  B, 
there  will  be  produced  within  the  coil  a  field  whose  direction,  as 
shown  by  the  broken  arrow,  is  from  above  downward.  In  ac- 
cordance with  Maxwell's  law  (Par.  371),  the  coil  will  turn  until 
it  embraces  its  own  field  and  that  of  the  magnet;  it  will  therefore 
take  up  a  counter-clockwise  rotation.'  The  turning  effect  of  the 
couple  mentioned  above  becomes  zero  when  the  coil  has  revolved 
until  it  lies  in  the  vertical  plane,  and  is  reversed  when  the  coil 
passes  through  this  plane.  The  coil  would  therefore  come  to  rest 
in  this  position.  However,  by  means  of  a  suitable  commutator, 


476  ELEMENTS  OF  ELECTRICITY. 

as  explained  under  generators  (Par.  556),  the  current  is  reversed 
as  the  coil  passes  through  the  vertical  plane;  its  field  is  therefore 
shifted  180°  ahead  and  the  rotation  becomes  continuous.  More- 
over, by  using  many  coils  upon  the  armature  (Par.  558),  it  is 
always  possible  to  have  the  current  flowing  through  those  in 
which  the  turning  effect  is  at  or  near  a  maximum. 

592.  Power  Developed  by  a  Motor. — Power  is  the  rate  at  which 
work  is  done  (Par.  492),  therefore 

work 

Power  =  — -. — 
time 

Work  is  force  exerted  over  a  path,  hence 

Power  =  f°rce  X  path 
time 

-  path 

=  force  X  IT— 
time 

=  force  X  velocity 

Consider  one  of  the  inductors  of  the  armature  of  a  motor  (Fig. 
^  ,    305).    The  force  exerted  upon  it  is  (Par.  591) 
f=I .  H  .1  dynes.     The  same  force  is  exerted 
upon  the  inductor  diametrically  opposite. 

If  r  be  the  radius  of  the  armature,  in  one 
complete  revolution  the  inductor  travels  a  dis- 
tance 2irr.  In  n  revolutions  it  travels  2irrn. 

If  these  n  revolutions  be  made  in  time  t,  the 
velocity  with  which  the  inductor  travels  is 

big.  305.  _          . 

2irrn/t. 

From  above,  power  =  forceX  velocity,  hence  power  developed 
by  the  motor  is 

P=2IHlx2irrn/t 
This  may  be  written 

P  =  IHlx2rX2>jm/t 

But  / HI X2r  =  armature  moment = torque,  and  2irn/t= angular 
velocity  of  the  armature,  hence  the  power  developed  varies  with 
the  torque  and  with  the  speed  of  rotation  of  the  armature. 

593.  Counter  Electro-Motive  Force. — Ignoring  for  the  moment 
the  cause  of  the  movement,  consider  a  rectangular  coil,  as  de- 
scribed in  Par.  591,  rotating  in  a  counter-clockwise  direction  in 


ELECTRO-MECHANICS.  477 

a  magnetic  field.  The  sides  of  this  coil  are  conductors  moving  in 
a  magnetic  field.  Application  of  the  right  hand  rule  (Fig.  306) 
will  show  that  there  is  induced  in  the  coil  an  E.  M.  F.  which  acts 
in  at  B  and  out  at  A.  The  more  rapid  the  rotation,  the  greater 
this  E.  M.  F.  (Par.  425).  Comparing  figures  306  and  304,  we  see 


Fig.  306. 


that  this  E.  M.  F.  is  opposed  to  that  of  the  current  which  causes 
the  motor  to  rotate;  in  other  words,  the  rotation  of  the  motor  sets 
up  an  E.  M.  F.  which  opposes  the  current  which  produces  the 
rotation.  This  opposing  E.  M.  F.  is  called  the  counter  or  back 
E.  M.  F. 

The  first  conspicuous  effect  of  the  counter  electro-motive  force 
developed  by  a  motor  is  to  cut  down  the  current  supplied.  If  an 
ammeter  be  connected  in  series  with  a  motor  and  the  circuit  be 
closed,  it  will  be  noted  that  before  the  motor  begins  to  move,  the 
current  is  very  large  (indeed,  without  some  special  arrangement 
to  be  described  later  [Par.  601]  it  may  be  excessive),  but  as  the 
motor  speeds  up,  the  current  falls  steadily. 

If  the  E.  M.  F.  applied  to  the  brushes  of  a  motor  be  E,  and  the 
resistance  of  its  armature  be  R,  the  current  through  the  armature 
before  the  motor  moves  is 


and  as  R  is  small,  I  is  great. 
As  the  motor  gains  speed,  the  current  becomes 

j  _  E  —  EB 
1  "     ~R~ 


478  ELEMENTS  OF  ELECTRICITY. 

or  only  so  much  as  can  be  driven  through  the  armature  by  the 
difference  of  the  impressed  and  the  back  E.  M.  F. 

594.  Relation  Between  Counter  E.  M.  F.  and  Power  Developed. 

— Since  the  power  which  a  generator  delivers  to  the  brushes  of  a 
motor  is  IE  watts  (Par.  494),  and  since,  as  shown  above,  7  is  cut 
down  by  the  back  E.  M.  F.  developed  and  hence  the  power  re- 
ceived by  the  motor  is  thereby  diminished,  it  would  seem  that 
back  E.  M.  F.  is  a  defect.  However,  consider  the  following: 

From  above,  the  current  which  a  generator  supplies  to  a  running 
motor  is  T  E-EB 

R 

whence          IR  =  E—EB 

whence          PR  =  IE-IEB 

whence          IE  =  I2R  +  IEB 

or    IE-,    the    total 

power  delivered  to  the  motor  by  the  generator,  is  divided  -into  two- 
parts,  one  of  which,  I2R,  represents  power  lost  in  heating  the 
armature  coils  (Par.  494);  the  other,  IEB,  represents  the  useful 
power  of  the  motor.  Hence,  the  useful  power  of  a  motor  is  direct- 
ly proportional  to  the  back  E.  M.  F.  which  it  develops. 

From  the  foregoing,  the  useful  power  of  a  motor  varies  with  the 
product  of  the  two  factors  /  and  EB.  In  Par.  592  it  was  shown 
that  this  power  also  varies  with  the  product  of  two  other  factors, 
the  torque  and  the  speed  of  rotation.  The  torque,  /  .  H  .  I  X  2r, 
if  the  field  H  be  constant,  varies  directly  with  the  current  /,  con- 
sequently, the  remaining  factor,  EB,  the  counter  E.  M.  F.,  varies 
directly  with  the  speed  of  rotation.  This  might  have  been  antici- 
pated since  we  have  shown  above  that  the  counter  E.  M.  F.  varies 
with  the  rate  at  which  the  lines  of  force  of  the  field  are  cut. 


VOLTMETER 


Fig.  307. 

595.  Reading  of  Voltmeter  Across  Seat  of  Counter  E.  M.  F. — 

There  is  sometimes  some  confusion  in  the  mind  of  a  beginner  as 
to  the  reading  of  a  voltmeter  shunted  around  a  seat  of  counter 
E.  M.  F.  The  correct  reading  is  always  the  sum  of  the  counter 


ELECTRO-MECHANICS.  479 

E.  M.  F.  and  of  the  regular  IR  drop  over  the  resistance  between 
the  two  points.  As  an  illustration,  let  G,  Fig.  307,  represent  a 
generator  connected  up  in  circuit  with  a  motor  M  across  whose 
brushes  a  voltmeter  is  shunted,  Let  the  E.  M.  F.  of  the  generator 
be  100  volts  and  suppose  its  resistance  to  be  negligible.  Let  the 
resistance  of  the  leads  be  one  ohm  and  that  of  the  motor  be  one 
ohm.  Suppose  that  the  generator  is  started  but  that  the  motor 
is  held  fast  and  not  allowed  to  rotate.  The  current  is  I  =  E/R  = 
100/2  =  50  amperes.  The  drop  over  the  leads  is  772  =  50  volts 
and  that  across  the  motor  is  /r  =  50  volts,  which  is  the  reading 
of  the  voltmeter.  Suppose  now  that  the  motor  is  released  and 
speeds  up,  producing  a  back  E.  M.  F.  of  90  volts.  The  current  is 

T     E-EB     100-90      c 
now  /  =  — o— -  =  — o =  5  amperes,  or  is  reduced  to  one-tenth 

K  Z 

of  what  it  was  originally.  The  IR  drop  over  the  leads  is  only  5 
volts;  the  reading  of  the  voltmeter  therefore  is  100  —  5=95  volts, 
that  is  90  for  the  back  E.  M.  F.  and  5  for  the  Ir  drop  across  the 
armature. 

596.  Efficiency  of  Motors. — A  generator  delivers  to  the  brushes 
of  a  motor  a  current  /  of  voltage  E.  The  resistance  across  the 
brushes  is  R.  The  motor  rotates  and  by  belts  or  gearing  or  other- 
wise turns  out  mechanical  power.  The  ratio  of  the  power  turned 
out  by  the  motor  to  the  power  delivered  to  its  brushes  by  the 
generator  is  the  measure  of  the  motor's  efficiency.  Thus,  if  the 
generator  supplies  ten  horse-power  to  the  motor  and  the  motor 
turns  out  nine  horse-power,  its  efficiency  is  9/10  or  90  per  cent. 

The  power  delivered  to  the  motor  is  IE  watts  (Par.  494) ;  the 
useful  power  turned  out  by  the  motor  is  IBs  watts  (Par.  594); 
the  efficiency  of  the  motor  is  therefore  measured  by  IEB/IE  or 
by  EB/E;  that  is,  the  nearer  the  counter  E.  M.  F.  approaches  the 
applied  E.  M.  F.,  the  greater  the  efficiency  of  the  motor. 

The  foregoing  may  be  shown  graphically  as  follows.  The  cur- 
rent through  the  motor  when  the  latter  is  running  is  (Par.  593) 

jr  =  E  -  EB 

Substituting  this  value  of  I  in  the  above  expressions,  we  obtain 
for  the  power  delivered  to  the  motor 

E(E  -  EB) 
R 


480 


ELEMENTS  OF  ELECTRICITY. 


and  for  the  power  turned  out  by  the  motor 

EB(E  - 


whence  the  efficiency  is 


R 


H 


E(E  -  EB) 

Upon  rectangular  axes  (Fig.  308)  lay  off  OA  =OB  propor- 
J  K  tional  to  EB,  and  OD=OF  propor- 
tional to  E.  Complete  the  squares. 
The  area  of  the  rectangle  ADJG, 
since  it  is  proportional  to  EB(E- 
EB),  is  proportional  to  the  power 
developed  by  the  motor.  The  area 
of  the  rectangle  BJKF,  since  it  is 
proportional  to  E(E—EB),  is  pro- 
portional to  the  power  delivered  to 
the  motor.  The  ratio  of  the  first  of 
these  rectangles  to  the  second  meas- 
Fig.  308.  ures  the  efficiency  of  the  motor.  The 

rectangle  BJKF  is  greater  than  ADJG  by  the  area  of  the  square 
JGKH.  The  efficiency  of  the  motor  approaches  unity  as  this 
square  diminishes,  which  it  does  as  OA  increases,  that  is,  the 
efficiency  of  the  motor  increases  as  the  counter  E.  M.  F.  increases. 
It  must  be  noted,  however,  that  as  the  counter  E.  M.  F.  OA  = 
OB,  increases,  the  current  through  the  motor  decreases,  and  the 
rectangles  representing  the  power  applied  and  the  power  turned 
out  both  diminish,  therefore,  so  long  as  the  motor  develops  ap- 
preciable power,  its  efficiency  is  never  perfect. 

597.  Maximum  Output  of  Power. — Maximum  efficiency  must 
not  be  confused  with  maximum  output  of  power.  From  the  pre- 
ceding paragraph,  the  power  turned  out  by  the  motor  is 


z  = 


R 


watts 


The  first  differential  coefficient  with  respect  to  EB  is 


Placing  this  equal  to  zero  and  solving  for  EB 


ELECTRO-MECHANICS.  481 

or  the  power  turned  out  by  a  motor  is  a  maximum  when  the 
counter  E.  M.  F.  is  equal  to  one-half  the  impressed  E.  M.  F.  In 
this  case  the  efficiency  is  only  one-half;  that  is,  there  is  a  loss  of 
one-half  of  the  power  delivered  to  the  motor. 

Reference  to  the  conclusion  drawn  in  Par.  340  will  show  that 
in  a  battery  also  when  the  power  developed  is  a  maximum,  the 
loss  is  one-half. 

598.  Classes  of  Direct-Current  Motors. — There  are  three  classes 
of  direct-current  motors,  the  series,  the  shunt  and  the  compound. 
The  majority  belong  to  the  first  two  of  these  classes.    In  structure 
they  are,  with  a  few  minor  changes,  the  same  as  the  correspond- 
ing generators.    Thus,  the  requirement  of  being  able  to  reverse 
the  direction  of  rotation  at  will  involves  the  setting  of  the  brushes 
at  right  angles  to  the  commutator  surface  instead  of  inclined  there- 
to.   So  also  in  the  operation  of  a  motor,  the  armature  reaction 
causes  the  brushes  to  be  shifted  backward  from  the  neutral  plane 
instead  of  forward  as  in  the  case  of  the  generators. 

As  a  rule,  motors  are  operated  on  constant  potential  circuits, 
the  voltage  between  the  mains  being  constant. 

599.  Shunt  Motors. — The  shunt  motor  possesses  certain  ad- 
vantages over  the  other  forms  which  render  it  by  far  the  most 
desirable  for  most  mechanical  purposes.     Chief  among  these  is 
its  ability,  as  shown  below,  to  make  automatic  adjustment  for 
fluctuations  in  the  load  thrown  upon  it  and  in  spite  of  these 
fluctuations  to  vary  but  little  in  speed. 


Fig.  309. 

Fig.  309  represents  in  simplest  diagrammatic  form  a  shunt  motor. 
The  difference  of  potential  between  A  and  B  being  constant,  as 
stated  above,  the  current  through  the  field  coil  AB  is  constant. 

The  force  on  the  several  inductors  of  the  armature  is  (Par.  592) 
/  =  /.  H  .1  dynes 

In  this  expression  H  and  I  are  constant,  hence  the  torque  varies 
directly  with  the  current  through  the  armature.  In  order  there- 
fore to  vary  the  torque  for  different  loads,  this  current  must  vary. 


482  ELEMENTS  OF  ELECTRICITY. 

The  current  through  the  armature  is  (Par.  593) 

I  =  E-EB 

From  this  we  see  that  the  current  can  be  increased  by  increas- 
ing E,  decreasing  EB,  or  decreasing  R.  Now  E  is  the  voltage 
between  the  mains,  which  we  have  seen  above  is  constant,  and  R 
is  the  armature  resistance,  which  is  fixed  when  the  machine  is 
built.  The  only  remedy  therefore  is  to  decrease  EB,  the  back 
E.  M.  F.  This  back  E.  M.  F.  varies  with  the  rate  at  which  the 
lines  of  force  of  the  field  are  cut  (Par.  594),  that  is,  it  varies 
directly  with  the  speed  of  rotation. 

When  the  load  upon  a  shunt  motor  is  suddenly  increased,  the 
speed  will  be  observed  to  decrease  slightly.  This  does  not  mean 
that  the  machine  is  weakening.  On  the  contrary,  by  slowing 
down,  the  back  E.  M.  F.  is  decreased,  the  current  and  hence  the 
torque  increase. 

A  numerical  example  will  bring  this  out  clearly.  If  in  the  above 
expression  for  the  current  we  make  £7  =  110,  £7^  =  100  and  R  =  l, 
we  get  7  =  10  amperes.  If  we  make  EB  =  9Q,  I  becomes  20 
amperes,  hence  a  reduction  of  one-tenth  in  the  speed  of  rotation 
doubles  the  torque  on  the  armature. 

Since  the  power  developed  by  the  motor  is  IEB  (Par.  594), 
it  may  be  asked  whether  the  increase  in  /  were  counterbalanced 
by  the  decrease  in  EB,  for  if  they  varied  reciprocally,  the  power, 
IEB,  might  remain  constant  and  nothing  would  be  gained. 
However,  I  increases  in  a  more  rapid  ratio  than  EB  decreases. 
In  the  numerical  example  above,  with  £5  =  100,  the  power  is 
1000  watts;  with  EB  =  90,  the  power  is  1800  watts. 

The  valuable  characteristic  of  the  shunt  motor  therefore  is 
that  by  slight  variations  in  speed  it  adjusts  itself  automatically 
for  wide  variations  in  the  load.  Even  should  the  load  be  suddenly 
entirely  taken  off,  the  motor  will  not  "race,"  or  speed  up  danger- 
ously. 

600.  Control  of  Speed  of  Shunt  Motors. — The  speed  at  which 
a  shunt  motor  runs  under  a  certain  load  may  be  controlled  in  one 
of  two  ways.  The  first  and  most  frequently  employed  method  is 
by  varying  the  strength  of  the  field.  There  is  inserted  in  the  field 
circuit  a  rheostat  by  which  the  current  through  the  field  coils  may 
be  varied.  By  increasing  the  resistance  in  this  circuit,  the  field 


ELECTRO-MECHANICS.  483, 

H  is  weakened.  This  causes  EB  to  diminish  and  the  current 
through  the  armature  consequently  increases.  The  torque,  IHlX 
2r  (Par.  592),  is  thus  increased  and  the  machine  speeds  up.  It  is 
true  that  the  torque  depends  also  upon  H,  but  we  have  shown  in 
the  preceding  paragraph  that  I  increases  more  rapidly  than  H 
decreases.  This  increase  of  speed  also  follows  from  the  fact  that 
if  the  field  be  weakened,  the  armature  must  revolve  faster  in 
order  to  cut  the  same  number  of  lines  of  force  in  the  same  time 
and  thus  develop  the  same  power. 

The  second  method  is  to  insert  between  the  motor  and  one  of 
the  mains,  as  shown  in  Fig.  310,  a  rheostat  R.    The  field  H  is  not 


B 


Fig.  310. 

affected  by  this,  but  the  voltage  applied  to  the  armature  is  the 
total  voltage  between  A  and  B  less  the  drop  over  the  rheostat. 
By  varying  the  resistance  in  R,  and  hence  the  drop  across  the 
rheostat,  the  voltage  between  C  and  B,  and  hence  the  current 
through  the  armature,  may  be  varied.  Since  the  torque,  IHlX 
2r,  H  remaining  constant,  varies  directly  with  /,  a  decrease  in 
the  current  decreases  the  speed  of  rotation, 

From  the  foregoing  it  is  seen  that  the  speed  of  a  shunt  motor 
may  be  increased  (a)  by  decreasing  the  current  through  the  field 
coils,  or  (b)  by  increasing  the  current  through  the  armature. 

It  should  be  remarked  that  control  by  rheostat  is  objectionable. 
The  power  consumed  in  heating  the  coils  of  the  rheostat  repre- 
sents pure  waste  which,  where  power  is  purchased,  must  be  paid 
for  just  as  if  it  were  doing  useful  work.  The  waste  in  the  second 
method  above,  since  a  larger  current  passes  through  the  rheostat, 
is  much  greater  than  that  in  the  first  method. 

601.  Starting-Box  for  Shunt  Motors. — It  was  stated  above, 
(Par.  593),  that  the  full  voltage  can  not  without  serious  risk  be 
turned  on  a  motor  at  rest.  It  is  customary  to  use  a  starting-box, 
a  form  of  rheostat  by  which,  as  the  back  E.  M.  F.  rises,  the  ap- 


484 


ELEMENTS  OF  ELECTRICITY. 


plied  E.  M.  F.  may  be  gradually  increased.  The  starting-box  for 
a  series  motor  does  not  differ  sufficiently  from  an  ordinary  rheostat 
to  warrant  a  special  description.  The  starting-box  for  a  shunt 
motor  possesses  certain  features  which  require  explanation. 

Although  for  these  motors  the  full  voltage  can  not  be  applied  at 
first  to  the  armature,  it  can  with  perfect  safety  be  applied  to  the 
field  coils.  This  enables  the  field  to  attain  its  full  strength  H  at 
once,  and  although  the  current  /  through  the  armature  be  small, 
the  torque  is  great  enough  to  cause  the  machine  to  gather  headway 
rapidly. 

Fig.  311  represents  diagrammatically  a  form  of  starting-box 
largely  used.  It  is  a  box-shaped  frame  with  lattice- work  sides  for 


Fig.  311. 

ventilation  and  contains  a  number  of  resistance  coils  in  series 
between  a  set  of  contacts  arranged  along  the  arc  of  a  circle  on 
the  marble  cover  of  the  box.  The  wire  of  the  coils  must  be  of 
sufficient  size  to  carry  the  current  required  by  the  motor,  and 
therefore  to  secure  the  necessary  resistance  they  have  to  be  long. 
An  iron  arm,  pivoted  at  P,  can  be  swept  along  over  the  contacts. 
At  the  pivot  of  this  arm  there  is  a  spring  which,  when  the  arm  is 
released,  throws  it  back  to  the  safety  position.  When  the  arm  is 
placed  on  the  first  contact  C,  the  current  from  the  positive  main 
comes  in  by  L,  thence  to  P,  thence  up  the  arm  to  C  where  it 
divides,  a  part  passing  through  all  the  resistance  coils  to  D,  thence 
to  A,  thence  to  the  armature  of  the  motor  and  thence  to  the 
negative  main,  and  the  other  part  passing  through  the  coil  H, 
thence  to  F,  thence  through  the  field  coils  to  the  negative  main. 
At  starting,  therefore,  the  current  through  the  armature  is  cut 
down  by  the  entire  resistance  of  the  coils  from  C  to  D,  while  the 


ELECTRO-MECHANICS.  485 

field  is  of  full  strength.  As  the  armature  begins  to  revolve  it 
generates  a  back  E.  M.  F.  and  it  becomes  safe  to  apply  more 
voltage.  The  arm  is  therefore  rotated  to  the  right  and  gradually 
cuts  out  the  resistance  in  the  armature  circuit. 

When  the  arm  is  hard  over  to  the  right,  the  entire  resistance  is 
out  of  the  armature  circuit  and  the  arm  is  held  by  the  electro- 
magnet H.  The  object  of  this  magnet  is  the  following.  Should 
the  circuit  be  broken  or  the  power  be  turned  off  while  the  motor 
is  in  operation,  the  arm  of  the  rheostat  should  be  automatically 
returned  to  the  safety  position,  otherwise  the  break  might  be 
repaired  or  the  power  be  turned  on  again  with  the  arm  in  its  full 
load  position  and  the  armature  coils  be  overheated  or  even  burned 
out.  When  a  break  occurs,  the  magnet  loses  its  power  and  the 
spring  at  P  throws  the  arm  back  to  the  safety  position.  This 
arrangement  is  called  a  "no  voltage  release." 

Again,  should  by  any  accident  the  current  through  the  field 
coils  be  greatly  reduced  or  entirely  cut  off  leaving  only  the  residual 
magnetism  of  the  field  magnets,  the  motor,  from  what  has  been 
shown  in  the  preceding  paragraph,  would  speed  up  dangerously, 
or,  if  this  did  not  occur,  would  not  generate  sufficient  back  E.  M. 
F.  to  keep  the  current  through  the  armature  down  to  safe  limits. 
Therefore,  in  this  case  also  the  rheostat  arm  should  be  automati- 
cally thrown  back  to  the  safety  position. 

It  will  be  noted  that  with  the  arm  hard  over  to  the  right,  the 
current  which  actuates  the  electro-magnet  H  is  the  field  current 
and  is  taken  off  by  the  upper  one  of  the  contacts  at  D.  Should 
a  break  occur  in  the  field  circuit,  this  magnet  releases  the  arm 
which  is  thrown  back  by  the  spring.  This  arrangement  is  called 
a  "no  field  release." 

These  starting-boxes  frequently  include  an  overload  switch  in 
addition  to  the  two  releases  described  above. 


Fig.  312. 

602.  Series  Motors. — In  a  series  motor,  shown  diagrammati- 
cally  in  Fig.  312,  the  same  current  passes  through  both  the  field 
coils  and  the  armature.  As  was  seen  in  the  discussion  of  the 


486 


ELEMENTS  OF  ELECTRICITY. 


magnetization  curve  (Par.  393),  at  first  and  when  remote  from 
saturation,  the  field  H  increases  nearly  in  proportion  to  the  ex- 
citing current,  hence,  at  starting,  the  torque  of  a  series  motor, 
I Hlx2r,  varies  practically  as  the  square  of  the  current.  These 
motors  are  therefore  especially  valuable  where  great  torque  is 
needed  at  starting,  for  example  in  trolley  cars,  hoists,  etc. 

603.  Speed  of  Series  Motors. — The  speed  of  series  motors 
varies  inversely  with  the  load  and  for  each  particular  load  there 
is  a  corresponding  speed.  This  renders  them  unsuitable  for  many 
kinds  of  machines  which  require  a  constant  speed  under  varying 
loads,  but  well  adapted  for  street  railways  where  the  speed  is  of 
necessity  constantly  varied. 

Consider  a  generator  supplying  a  series  motor  M  (Fig.  313). 
The  power  developed  by  the  motor  must  be  equal  to  that  sup- 


Fig.  313. 

plied  by  the  generator,  less  the  heat  loss.  This  last  is  small,  hence 
the  back  E.  M.  F.  must  be  nearly  equal  to  the  impressed  E.  M.  F. 
As  the  back  E.  M.  F.  increases,  the  current  through  the  motor, 
and  hence  the  current  through  the  field  coils,  grows  smaller.  The 
field  grows  correspondingly  weaker  and  to  maintain  the  back 
E.  M.  F.  the  speed  of  the  motor  must  increase.  This  tendency  to 
race  under  diminished  loads  is  an  objectionable  feature  of  a  series 
motor. 

604.  Change  of  Direction  of  Rotation. — It  may  sometimes  be 
desirable  to  change  the  direction  of  rotation  of  a  motor.  Suppose 
a,  Fig.  314,  to  represent  a  shunt  motor,  the  current  flowing  as 

b 


'* ;-- ' 

Fig.  314. 

indicated.  The  lines  of  force  of  the  coil  will  run  upwards  and  the 
rotation  will  therefore  be  clockwise.  If  the  direction  of  the  cur- 
rent in  the  mains  be  reversed,  as  shown  in  6,  the  lines  of  force  of 


ELECTRO-MECHANICS.  487 

the  coil  will  run  downward,  but  the  polarity  of  the  field  magnets 
is  also  reversed,  and  the  rotation  will  as  before  be  clockwise. 
Hence,  reversing  the  current  in  the  mains  does  not  change  the 
direction  of  rotation.  If,  however,  the  direction  of  the  current 
be  reversed  in  either  the  field  or  the  armature,  but  not  in  both, 
the  direction  of  rotation  will  be  changed. 

605.  Motor  Generators. — Alternating  currents  are  readily 
stepped  up  or  down  in  voltage  by  means  of  a  transformer  (Par. 
431),  but  this  method  is  not  applicable  to  direct  currents.  Where 
such  transformation  is  required,  the  direct  current  may  be  em- 
ployed to  operate  a  motor  and  this  motor  in  turn  operates  a  gener- 
ator whose  armature  is  so  wrapped,  or  whose  field  is  of  such 
strength,  as  to  develop  a  current  of  the  desired  voltage.  Instead 
of  having  the  motor  rotate  the  generator  by  means  of  a  belt  or 
gearing,  they  may  both  be  mounted  upon  a  common  shaft.  This 
combination  is  called  a  motor  generator,  but  electrically  it  is  the 
same  as  two  separate  machines. 

A  step  further  may  be  taken  and  two  sets  of  coils  may  be 
wrapped  upon  the  same  armature  and  rotate  in  a  common  field. 
Each  set  has  its  own  commutator,  current  being  delivered  to  the 
motor  commutator  and  drawn  from  the  generator  commutator. 
Transformation  is  effected  by  varying  the  ratio  of  the  number 
of  coils  or  of  the  number  of  turns  in  the  two  sets  of  wrappings. 
This  machine  is  called  a  dynamotor. 


488  ELEMENTS  OF  ELECTRICITY. 


CHAPTER  43. 

ALTERNATING    CURRENTS. 

606.  Alternating  E.  M.  F.  and  Current. — We  have  seen  (Par. 
552),  that  if  a  coil  rotates  at  a  uniform  rate  in  a  uniform  field  it 
will  generate  an  E.  M.  F.  which  varies  as  the  sine  of  the  angle 
through  which  the  coil  has  turned  from  its  primary  position  at 
right  angles  to  the  field.    If  the  coil  is  a  closed  circuit,  or  forms  a 
part  of  such  a  circuit,  there  will  be  produced  in  it  a  current  which 
will  vary  in  the  same  manner.    At  every  revolution  of  the  coil, 
therefore,  the  E.  M.  F.  and  current  pass  through  a  complete  cycle 
of  values,  positive  and  negative.    The  term  alternating  is  applied 
to  an  E.  M.  F.,  or  to  a  current,  which  thus  undergoes  these  periodic 
reversals. 

607.  Why  Considered  Separately. — The  mere  fact  that  a  cur- 
rent reverses  its  direction  at  regular  intervals  might  not  of  itself 
warrant  special  discussion.    There  are,  however,  two  properties, 
induction  and  capacity,  which  are  common  to  all  electric  circuits 
and  whose  effects  are  conspicuously  revealed  in  varying  currents. 
Alternating  currents  vary  continually  and  with  such  currents  the 
above  factors  give  rise  to  certain  peculiar  phenomena,  some  of 
which  appear  to  contradict  the  principles  which  have  been  developed 
in  the  preceding  pages.    Among  such  we  may  mention 

(a)  The  current  through  a  circuit  is  not  always  equal  to  the 
E.  M.  F.  divided  by  the  resistance. 

(b)  The  sum  of  the  partial  drops  between  two  points  is  not 
always  the  same  as  the  total  drop. 

(c)  The  sum  of  the  currents  in  the  branches  of  a  divided  circuit 
is  not  always  equal  to  the  total  current. 

(d)  Finally,  there  may  be  a  flow  of  current  in  a  broken  circuit. 
In  the  following  pages  it  will  be  shown  that  these  contradictions 

are  only  apparent  and  that  Ohm's  law  is  as  true  of  alternating 
currents  as  it  is  of  direct.  In  order,  however,  to  be  able  to  explain 
these  peculiarities,  the  subject  of  alternating  currents  must  be 
considered  in  detail.  We  shall  therefore  begin  with  certain  pre- 
liminary definitions  and  principles. 


ELECTRO-MECHANICS.  489 

608.  Cycle,  Period  and  Frequency. — In  Par.  555  it  was  shown 
that  an  alternating  E.  M.  F.  and  current  can  be  represented 
graphically  by  a  sine  curve  (Fig.  315),  the  ordinates  corresponding 
to  the  instantaneous  values  (values  at  any  instant)  of  the  E.  M.  F. 
or  current  and  the  abscissae  to  the  angle  through  which  the  coil 


Fig.  315. 

has  rotated,  or,  if  the  scale  of  time  be  used,  to  the  time  elapsed 
since  the  coil  moved  from  its  primary  position  in  the  neutral 
plane. 

If  Em  be  the  maximum  instantaneous  value  of  the  E.  M.  F.  and 
if  the  abscissae  represent  the  angle  through  which  the  coil  has 
rotated,  the  equation  of  the  E.  M.  F.  curve  is 

E  =  Em  .  sin  6 
If  the  abscissae  represent  elapsed  time,  the  equation  is 

E  =  Em  .  sin  ut 

in  which  o>  is  the  angular 

velocity  of  the  coil  and  t  is  the  time  in  seconds  since  the  coil  lay 
in  the  neutral  plane. 

With  every  revolution  of  the  coil,  the  portion  of  the  curve  be- 
tween A  and  B  (Fig.  315)  is  repeated,  and  the  complete  set  of 
values,  positive  and  negative,  between  A  and  B  is  therefore  called 
a  cycle.  The  more  rapid  the  motion  of  the  coil,  the  greater  the 
number  of  cycles  in  a  given  time.  The  lengths  of  time  of  one  cycle 
is  called  a  period  and  the  number  of  cycles  per  second  is  the 
frequency.  The  word  "revolution,"  as  used  above,  must  be  inter- 
preted in  an  electric  sense.  Thus,  in  a  four  pole  generator  one 
revolution  of  the  armature  corresponds  to  two  electric  revolutions. 

An  additional  term,  sometimes  encountered  in  books  treating 
of  this  subject,  is  alternation,  an  alternation  being  a  reversal  of 
direction  of  E.  M.  F.  or  current.  There  are  therefore  two  alter- 
nations per  cycle.  The  number  of  alternations  is  usually  given  as 
so  many  per  minute.  It  is  recommended  that  the  use  of  this  term 
be  discarded. 


490 


ELEMENTS  OF  ELECTRICITY. 


609.  Phase. — For  purposes  of  descriptive  location,  a  cycle  is 
considered  to  be  divided  into  360  degrees.  Any  point  of  the  cycle 
is  designated  as  a  certain  phase,  as,  for  example,  the  thirty  degree 
phase,  etc. 

Fig.  316  represents  diagrammatically  a  ring-wound,  bipolar, 
alternating  current  generator.  Consider  in  either  half  of  the 


Fig.  316. 

armature  any  two  adjacent  coils,  as,  for  example,  B  and  C.  In 
each  an  E.  M.  F.  is  being  induced  and  since  in  every  complete 
revolution  of  the  armature  each  coil  travels  around  the  same  path 
and  returns  to  its  starting  point,  the  cycle,  the  period  and  the 
frequency  must  be  the  same  for  each.  At  the  instant  shown  how- 
ever, the  E.  M.  F.  being  induced  in  C  is  proportional  to  the  sine 


Fig.  317. 

of  the  angle  CO  A,  while  that  being  induced  in  B  is  proportional  to 
the  sine  of  BOA,  and  will  not  reach  the  value  of  that  now  in  C 
until  sufficient  time  has  elapsed  for  B  to  move  through  the  angle 
0=  BOC.  The  E.  M.  F.  in  C  therefore  has  reached  a  value  which 


ELECTRO-MECHANICS.  491 

will  not  be  reached  by  that  in  B  for  a  time  corresponding  to  the 
angle  <£.  This  is  shown  graphically  in  Fig.  317.  The  sine  curve 
CCCCC  represents  the  E.  M.  F.  of  the  coil  C;  the  sine  curve 
BBBBB  represents  the  E.  M.  F.  of  the  coil  B. 

Two  sine  curves  whose  periods  are  the  same  and  which  reach 
their  maximum  and  minimum  values  simultaneously  (see  Fig.  265) 
are  said  to  be  in  phase,  otherwise  they  are  said  to  differ  in  phase. 
The  phase  difference  may  be  expressed  in  time  but  more  frequently 
in  angular  measure.  Thus,  the  curves  in  Fig.  317  differ  in  phase 
by  the  angle  <f>  which  is  represented  by  the  horizontal  distance 
CB.  If  the  phase  difference  is  90°,  the  curves  are  said  to  be  in 
quadrature;  if  it  be  180°,  they  are  in  opposition. 

It  will  be  shown  shortly  that  an  alternating  current  generally 
differs  in  phase  from  its  corresponding  E.  M.  F.  If  the  current 
reaches  a  maximum  value  after  the  E.  M.  F.  has  passed  through 
its  maximum,  the  current  is  said  to  lag;  on  the  other  hand,  if  it 
reaches  its  maximum  in  advance  of  the  E.  M.  F.,  it  is  said  to  lead. 
In  these  cases,  the  corresponding  phase  difference  is  spoken  of  as 
the  angle  of  lag  or  as  the  angle  of  lead. 

610.  Vector  Diagrams.— Let  the  vector  OA  (Fig.  318),  whose 
length  represents  the  maximum  value 
Em  of  an  alternating  E.  M.  F.  (or  cur- 
rent), rotate  about  the  point  0  in  a 
counter-clockwise  direction  and  at  the 
same  uniform  angular  velocity  co  as 
the  armature.  The  instantaneous  value 


of  the  E.  M.  F.  (or  current)  is  repre-  Fi§-  318- 

sented  by  the  line  A  B,  for  AB  =  Em  .  sin  at.  But  DO,  the  pro- 
jection of  OA  upon  the  vertical  axis,  is  equal  to  AB,  hence,  when 
the  vector  makes  the  phase  angle  with  the  horizontal  axis,  the 
corresponding  instantaneous  value  of  the  E.  M.  F.  (or  current) 
is  represented  by  the  projection  of  the  vector  upon  the  vertical 
axis. 

611.  Composition  of  Alternating  E.  M.  F.s. — During  the  rota- 
tion of  the  armature  of  the  generator  shown  in  Fig.  316,  the  coils 
in  series  combine  in  producing  a  resultant  E.  M.  F.  Thus,  in  Fig. 
317  the  broken  and  dotted  curve  is  the  resultant  E.  M.  F.  curve 
obtained  by  adding  the  ordinates  representing  the  corresponding 
simultaneous  values  of  the  E.  M.  F.  in  the  separate  coils.  By  an 


492  ELEMENTS  OF  ELECTRICITY. 

application  of  trigonometry,  it  can  be  shown  that  this  resultant 
curve  is  also  a  sine  curve  and  is  of  the  same  periodicity  as  the 
component  curves,  although  differing  from  them  in  phase.  The 
trigonometric  process  is  somewhat  tedious  and  it  is  thought  that 

the   following   explanation    will    be 
more  easily  followed.     In  Fig.  319, 

,  w  „.      /    ,  the  vectors  OB  and  OC  represent  the 

'    /  maximum  values  of  the  E.  M.  F.  in 

the  coils  B  and  C  of  Fig.  316,  and  0 
is  the  angle  of  phase  difference.  The 
instantaneous  value  of  the  E.  M.  F. 
in  B  is,  from  the  preceding  para- 
Fig.  319.  graph,  OB'',  the  instantaneous  value 
of  the  E.  M.  F.  in  C  is  OC',  and  the  resultant  E.  M.  F.  is  the  sum 
of  OB'  and  OC'.  Complete  the  parallelogram  CDBO  and  project 
its  diagonal  OD  upon  the  vertical  axis.  C'D'  is  equal  to  OB', 
hence  OD'  is  equal  to  the  sum  of  OB'  and  OC',  or  is  the  desired 
resultant.  Therefore,  the  resultant  E.  M.  F.  of  the  coils  B  and  C 
is  always  given  by  the  projection  upon  the  vertical  axis  of  the 
vector  OD,  the  diagonal  of  a  parallelogram  of  which  the  adjacent 
sides  represent  the  maximum  values  of  the  E.  M.  F.  in  the  corre- 
sponding coils  and  the  included  angle  represents  the  difference  in 
phase.  The  length  of  OD  represents  the  maximum  value  of  the 
resultant  E.  M.  F.  Since  <£,  the  difference  in  phase,  is  constant, 
the  vector  OD  does  not  vary  in  length  or  in  position  relative  to 
OB  and  OC.  Its  projections  are  therefore  the  ordinates  of  a  sine 
curve  of  the  same  periodicity  as  the  E.  M.  F.  curves  of  the  separate 
coils. 

From  the  foregoing  we  see  that  alternating  E.  M.  F.s  which 
differ  in  phase  are  not  compounded  by  simple  addition  but  in  a 
similar  manner  to  that  employed  in  the  parallelogram  of  forces  in 
mechanics. 

612.  Value  of  an  Alternating  Current. — During  each  cycle,  an 
alternating  current  passes  through  the  entire  range  of  values  from 
zero  to  the  positive  maximum,  thence  through  zero  to  the  mini- 
mum (negative  maximum),  thence  back  to  zero.  Which  of  all 
these  values  should  be  taken  as  a  measure  of  the  current?  The 
logical  agreement  is  reached  that  such  a  current  is  equal  to  that 
direct  current  which  performs  the  same  amount  of  work  in  the 
same  length  of  time.  Of  the  three  classes  of  work  which  a  current 


ELECTRO-MAGNETICS. 


493 


may  perform  (Par.  444),  only  one,  the  heating  effect,  is  inde- 
pendent of  the  direction  of  the  current,  and  this  is  accordingly 
selected  as  the  basis  of  comparison. 


A 


M    N 


Fig.  320. 

Let  the  curve  AB  (Fig.  320)  represent  an  alternating  current 
produced  by  a  coil  rotating  with  an  angular  velocity  co.  If  the 
maximum  value  of  the  current  be  Im,  the  equation  of  this  curve  is 

I  =  Im  .  sin  ut  (I) 

Consider  any  ordinate  of  this  curve  as  /.  The  instantaneous 
value  of  the  power  being  developed  at  this  point  is  PR  (Par.  494), 
R  being  the  resistance  of  the  circuit  through  which  the  current  is 
flowing.  Let  M  N  represent  a  minute  interval  of  time  dt.  Since 
work  =  power  Xtime,  the  work  done  by  I  during  this  interval  is 

dw^PR  .dt 

Substituting  in  this  the  value  of  /  from  (I) 
dw  =  fmR  .  sin2o>£ .  dt 

The  integral  of  this  between  the  proper  limits  will  give  the  total 
work  performed  by  the  current  during  the  cycle. 


Jsin'W.  (co  dt) 


CO 


( —  \  cos  u>t .  sin 


a  constant 


Taking  this  between  the  limits  ut  =  0  and  ut  = 


CO 


(ID 


Hence  7=        =  0.707  I 


494  ELEMENTS  OF  ELECTRICITY. 

The  work  performed  by  a  direct  current  flowing  through  the 
same  resistance  for  the  same  length  of  time  is 

w  =  PRt 

A 

Since  at  =  2ir,  t,  the  time  of  one  cycle  =  — 

CO 

Substituting,  we  have 

w=/2#.—  (Ill) 

CO 

Equating  the  second  members  of  (II)  and  (III) 
/2#.  —  =I2mR.- 

CO  CO 

m 

that  is,  the  alternating  current  is 

equivalent  to  a  direct  current  whose  value  is  only  .707  of  the  maxi- 
mum value  of  the  alternating  current.  This  may  be  otherwise 
expressed  by  saying  that  the  effective  or  virtual  value  of  the  alter- 
nating current  is  only  .707  of  its  maximum  value.  The  same 
relation  exists  between  the  effective  and  the  maximum  voltage  of 
an  alternating  current,  and  ammeters  and  voltmeters  for  use  with 
such  currents  are  graduated  to  read  the  virtual  amperes  and  volts 
respectively. 

613.  Second   Deduction.  —  The   foregoing   deduction   may   be 
made  without  the  use  of  the  calculus,  as  follows: 

Let  AA  and  BB  (Fig.  321)  be  two 
coils  at  right  angles  to  each  other,  both 
rotating  at  a  uniform  rate  in  a  uniform 
field  and  each  sending  current  through  a 
resistance  #.  In  one  complete  revolution 
the  work  done  by  the  currents  from  both 
/^''"  \  /  is  twice  the  work  done  by  the  current 

\  \         /'        from  one.    The  current  from  A  being 

X^  v*  .S'  ?m  sm  0»  that  from  B  is  Im  cos  0.    The 

"p"~T~     B  power  developed  at  any  instant  by  the 

current  from  A  is  I2msin^&R;  that  de- 

veloped at  the  same  instant  by  the  current  from  B  is  I2m  cos2  0  R. 
The  total  instantaneous  power  is  the  sum  of  these  two,  or 

Jj,  (sin2  6  +  cos2  0)  R  =  fm  R 


ELECTRO-MECHANICS.  495 

The  total  work  done  during  the  time  t  of  one  complete  revolu- 
tion is  fm  Rt,  hence  the  work  done  in  this  time  by  the  current  from 
one  coil  is  \  1^  Rt.  A  direct  current  /  flowing  for  a  time  t  through 
the  resistance  R  does  work  P  Rt. 


=  ^  I2m  Rt 


Hence 

= 
V2 


/  =  —^  as  before. 


614.  Self-Induction.  —  Self-induction  was  explained  in  detail 
in  Pars.  432-436  and  it  was  shown  that  its  characteristic  effect  is 
to  oppose  any  change  in  a  current-produced  field  and  that  it  does 
this  by  setting  up  a  counter  E.  M.  F.  which  opposes  any  change  in 
the  current  in  the  circuit  involved.  Since  alternating  currents  are 
always  changing,  it  is  in  dealing  with  such  currents  that  the  con- 
sideration of  induction  assumes  the  greatest  importance. 


Fig.  322. 

If  an  alternating  E.  M.  F.  be  applied  to  a  circuit  of  a  simple  loop 
of  wire  (Fig.  322  a),  the  effect  of  induction  may  be  so  slight  as  to 
be  negligible  and  the  current  may  be  considered  to  follow  Ohm's 
law. 

If  the  same  piece  of  wire  be  wrapped  into  a  coil  of  100  turns  and 
the  E.  M.  F.  be  applied  so  as  to  produce  the  same  number  of  lines 
of  force  in  the  field  in  the  same  time  as  before,  these  are  now  cut 
one  hundred  times  instead  of  once  and  the  effect  of  induction  is 
one  hundred  times  as  great. 

Finally,  if  there  be  inserted  in  this  coil  a  soft  iron  core  (Fig. 
322  b)  and  the  E.  M.  F.  be  applied,  the  same  change  of  current 
will  produce  about  2000  times  as  many  lines  of  force  (Par.  394) 
and  the  effect  of  induction  will  be  200,000  times  as  great  as  in  the 
first  case.  These  examples  show  that  self-induction  is  developed 
by  the  cutting  of  the  lines  of  force  in  the  embraced  field  rather 
than  by  changes  in  the  current  in  the  embracing  circuit. 

615.  Inductance. — Self-induction  is  measured  by  the  cutting 
of  lines  of  force  produced  when  the  current  in  the  circuit  is  varied 
one  unit.  The  practical  unit,  the  henry,  is  the  self-induction  of 


496  ELEMENTS  OF  ELECTRICITY. 

that  circuit  in  which  a  change  of  one  ampere  produces  a  cutting  of 
108  lines  of  force.  When  the  self-induction  of  a  circuit  is  expressed 
numerically,  as  so  many  henrys,  it  is  called  inductance.  The  in- 
ductance of  a  given  circuit  is  constant  provided  the  circuit  is 
distant  from  magnetic  bodies.  If  it  be  not  distant  from  such 
bodies,  owing  to  their  saturation,  the  field  does  not  vary  uniformly 
with  the  current. 

Although  the  inductance  is  thus  constant,  the  counter  E.  M.  F. 
which  it  is  instrumental  in  producing,  and  whose  effect  is  so  im- 
portant, is  not  at  all  constant  but  varies  with  the  rate  of  change 
of  the  current  (Par.  432)  and  has  therefore  a  different  value  at 
every  different  phase  and  for  every  different  frequency  employed. 
This  will  be  shown  more  clearly  later  on. 

616.  Inductance  and  Resistance. — Inductance  and  resistance 
agree  in  that  they  oppose  the  flow  of  current  in  a  circuit,  but  here 
the  similarity  ends.    The  following  will  bring  out  the  difference 
between  the  two. 

(a)  The  resistance  of  a  circuit  is  constant  and  does  not  vary 
with  changes  in  the  current.    The  inductance  of  a  circuit  appears 
only  when  the  current  is  changing  and  the  counter  E.  M.  F.  which 
it  sets  up  is  proportional  to  the  rate  of  this  change. 

(b)  Resistance  does  not  vary  with  the  geometric  form  of  the 
circuit  nor  with  the  proximity  of  magnetic  bodies.    Inductance 
depends  essentially  upon  these  factors. 

(c)  The  energy  spent  in  overcoming  resistance  is  lost  in  the 
form  of  heat.    That  spent  in  overcoming  the  induction  counter 
E.  M.  F.  (Par.  359)  is  periodically  absorbed  in  the  field  about  the 
conductor  as  the  current  rises  and  is  restored  to  the  circuit  as  the 
current  falls.    As  an  analogy,  the  energy  spent  upon  a  fly-wheel 
does  two  things:  (1)  it  overcomes  the  friction  of  the  bearings  and 
is  thus  lost  as  heat,  and  (2)  it  is  absorbed  by  the  wheel  which, 
after  the  power  is  shut  off,  continues  to  turn  and  thus  restores 
the  absorbed  energy. 

All  circuits  contain  resistance,  inductance  and  capacity,  but 
one  or  more  may  be  so  small  as  to  be  negligible.  For  the  sake  of 
simplicity  we  shall  first  consider  a  circuit  in  which  the  capacity 
may  be  disregarded. 

617.  Alternating  E.  M.  F.  in  a  Circuit  Having  Resistance  and 
Inductance. — The  instantaneous  value  of  the  current  produced 


ELECTRO-MECHANICS.  497 

in  a  coil  rotating  at  a  uniform  rate  in  a  uniform  field  is  (Par.  612) 

I  =  Im  .sin  coZ 

In  this  expression,  co  is  the  angular  velocity  of  the  moving  coil, 
whence  (d  is  the  angular  distance  through  which  the  coil  rotates 
in  t  seconds.  In  one  revolution  the  coil  turns  through  the  angle 
27T.  If  the  frequency  be  /,  that  is,  if  the  coil  makes  /  revolutions 
per  second,  the  angular  distance  through  which  it  travels  in  one 
second  is  2?r/  and  in  t  seconds  is  2irft.  We  may  therefore  sub- 
stitute 2irjt  for  ut  in  the  above  expression,  whence 

I  =  Im  .  sin  2irft 

If  the  resistance  of  the  circuit  be  R,  the  E.  M.  F.  required  to 
drive  the  current  /  through  this  resistance  is,  from  Ohm's  law, 
ER  =  IR,  or,  substituting  the  above  value  of  I 


This  E.  M.  F.,  which  is  variously  called  the  active,  the  efficient, 
or  the  power  E.  M.  F.,  reaches  its  maximum  value  ImR  when 
sin  2irft=  1,  that  is,  at  the  90°  and  the  270°  phases,  or  at  B  and  D 
(Fig.  323),  and  may  be  represented  by  the  sine  curve  AFCGE, 
the  corresponding  current  being  in  phase  with  it  and  being  repre- 
sented by  the  sine  curve  ASCTE. 

Should  there  be  in  the  circuit  an  inductance  of  L  henry,  there 
will  be  produced  a  counter  E.  M.  F.  whose  value  is  (Par.  434) 

F  Tdl 

EB  =  ~Ldf 

Since  from  above 

I  =  Im  .  sin  2irft 


whence 

EB=  -L.Im.  2irf.  COS 

This  counter  E.  M.  F.  may  therefore  be  represented  by  a  sine 
curve.  It  reaches  its  maximum  value  Im  .  2wfL  when  cos  2irft  =  1, 
that  is,  at  the  0°  and  the  180°  phases,  or  at  A,  C  and  E  (Fig.  323). 
It  is  therefore  in  quadrature  with  the  E.  M.  F.  represented  by 
the  curve  AFCGE.  Also,  since  this  E.  M.  F.  opposes  any  change 
in  the  existing  current,  it  is  positive  as  the  latter  falls  and  negative 
as  the  latter  rises.  It  is  a  maximum  when  the  current  passes 


498 


ELEMENTS  OF  ELECTRICITY. 


through  zero,  since  at  this  moment  the  rate  of  change  of  the  cur- 
rent is  greatest,  and  it  is  zero  when  the  current  is  a  maximum, 
either  positive  or  negative.  It  may  therefore  be  represented  by 
the  sine  curve  HBJDK.  . 


Fig.  323. 

In  order  to  drive  the  current  /  through  the  circuit,  the  im- 
pressed E.  M.  F.  must  be  greater  than  that  required  by  Ohm's 
law  of  a  direct  current,  for  it  must  not  only  be  sufficient  to  over- 
come the  ohmic  resistance  but  also  to  counterbalance  the  back 
E.  M.  F.  due  to  self-induction. 

The  curve  LBMD  N  represents  the  E.  M.  F.  required  to  over- 
come the  counter  E.  M.  F.  Its  ordinates  are  equal  but  of  opposite 
sign  to  the  corresponding  ordinates  of  the  curve  HBJDK.  The 
impressed  E.  M.  F.  is  the  resultant  obtained  by  compounding 
the  E.  M.  F.  represented  by  the  curve  AFCGE  and  that  repre- 
sented by  the  curve  LBMD  N.  The  curve  LPFMQG  N,  obtained 
by  adding  the  corresponding  ordinates  of  these  two  curves, 
represents  this  resultant.  It  will  be  noted  that  it  reaches  its 
maximum  at  P  before  the  current  reaches  its  maximum  at  S, 
that  is,  it  leads  the  current  by  a  difference  of  phase  correspond- 
ing to  RE.  In  alternating  current  circuits  containing  resistance 
and  inductance  alone,  the  current  always  lags  behind  the  im- 
pressed E.  M.  F. 

618.  Graphic  Construction  of  E.  M.  F.  and  Current  Curves.— 

The  power  E.  M.  F.,  or  E.  M.  F.  required  to  overcome  the  ohmic 
resistance,  and  the  E.  M.  F.  required  to  counterbalance  the 
E.  M.  F.  of  self-induction,  may  be  compounded  as  just  explained. 
They  may  also  be  compounded  according  to  the  method  described 
in  Par.  611.  Thus,  to  find  the  instantaneous  values  of  the  various 


ELECTRO-MECHANICS. 


499 


E.  M.  F.s  and  current  at  any  phase,  such  as  x,  Fig.  324.  Lay  off 
oa  to  represent  the  maximum  value,  ImR,  of  the  power  E.  M.  F. 
and  making  with  the  horizontal  axis  an  angle  6  corresponding  to 
the  phase  angle  Ex.  On  this  same  line,  since  the  current  is  in 
phase  with  this  E.  M.  F.,  lay  off  oc  to  represent  the  maximum 
value  Im  of  the  current.  Lay  off  ob  at  right  angles  to  oa  (the 
two  E.  M.  F.s  being  in  quadrature)  and  of  a  length  to  represent 
the  maximum  value,  ImZirfL,  of  the  E.  M.  F.  to  overcome  the 
E.  M.  F.  of  self-induction.  The  diagonal  od  of  the  parallelogram 
constructed  upon  oa  and  ob  is  the  vector  corresponding  to  the 
required  impressed  E.  M.  F.  The  projection  of  oa  upon  the 


Fig.  324. 


ordinate  at  x  locates  the  point  A  of  the  curve  of  power  E.  M.  F., 
that  of  ob  locates  the  point  B  of  the  curve  of  E.  M.  F.  to  counter- 
balance the  induced  E.  M.  F.,  and  that  of  od  locates  the  point  D 
of  the  curve  of  impressed  E.  M.  F.  Finally,  the  projection  of  oc 
upon  the  ordinate  at  x  locates  the  point  C  of  the  current  curve. 

619.  Inductive  Reactance. — The  counter  E.  M.  F.  due  to  self- 
induction  varies  with  the  rate  at  which  the  lines  of  force  are  cut. 
It  therefore  varies  not  only  with  the  inductance,  or  number  cut 
when  the  current  is  varied  one  ampere,  but  also  with  the  rapidity 
with  which  the  current  changes.  In  alternating  currents  this  is 
a  function  of  the  number  of  cycles  per  second,  that  is,  of  the 
frequency.  In  Par.  617  it  was  shown  that  this  E.  M.  F.,  which 
is  also  called  the  reactive  E.  M.  F.,  is  in  quadrature  with  the  power 
E.  M.  F.  and  that  its  maximum  value  is 

EB  =  / 


500 


ELEMENTS  OF  ELECTRICITY. 


The  factor,  2irfL,  is  called  the  inductive  reactance.  It  obviously 
varies  with  the  frequency  /  and  with  the  inductance  L.  It  is 
measured  in  ohms,  as  might  be  inferred  from  the  fact  that  when 
multiplied  by  current  the  product  is  E.  M.  F.  By  expressing 
it  in  its  dimensional  formula,  it  may  be  shown  to  be  of  the  same 
dimensions  (a  velocity)  as  resistance  (Par.  547).  It  is  sometimes 
defined  as  that  factor  by  which  the  maximum  value  of  an  alternat- 
ing current  in  a  circuit  containing  inductance  is  multiplied  in 
order  to  obtain  the  maximum  value  of  the  reactive  E.  M.  F.  The 
reactance  of  a  circuit  for  a  given  frequency  is  obtained  in  ohms 
by  multiplying  the  inductance  in  henrys  by  2w  times  the  frequency. 

620.  Impedance. — Examination  of  Fig.  324  will  show  that  od, 
the  maximum  value  of  the  impressed  E.  M.  F.,  is  the  hypothe- 
nuse  of  a  right-angled  triangle  whose  sides  are  oa  =  ImR,  the 
maximum  value  of  the  power  E.  M.  F.,  and  ad  =  ob  =  Im.2irfLf 
the  maximum  value  of  the  reactive  E.  M.  F.  It  follows  that 

(Fig.  325  a)  ^  _  (r   p\2_L/7    o  tr\* 

&m  =  (ImJK)    -p  \JLm3tfFjlj) 

whence  ^m 

Im=  V#2  +  (27r/L)2 

The  resemblance  of  this  expression  to  Ohm's  law  is  obvious. 
The  denominator  of  the  fraction  in  the  second  member  is  meas- 
ured in  ohms  since  it  is  composed  of  the  resistance  and  the  re- 


Fig.  325. 

actance,  both  of  which  are  measured  in  ohms.  It  is  called  the 
impedance  since  it  represents  the  combined  effect  of  the  ohmic 
resistance  and  the  reactance  in  impeding  the  flow  of  the  current. 
It  is  sometimes  defined  as 'that  factor  by  which  the  current  in  an 
alternating  circuit  is  multiplied  in  order  to  get  the  corresponding 
impressed  E.  M.  F.  It  will  be  noted  that  if  /=0,  the  current 
becomes  direct  and  the  expression  reduces  to  Ohm's  law. 


ELECTRO-MECHANICS.  501 

Inspection  of  the  expression  will  show  that  the  impedance  is 
itself  the  hypothenuse  of  a  right-angled  triangle  whose  sides 
are  the  resistance  and  the  reactance  (Fig.  325  6). 

It  is  also  seen  that  the  angle  of  lag,  doc  (Fig.  324),  is  given  by; 
the  relation 

da     2-7T/L      reactance 
tan  <b  =  —  =  — ^r—  =  — 

oa        R        resistance 

and  also  by  the  relation 

oa      Ej^  _      power  E.  M.  F. 
od  ~  Em  ~  impressed  E.  M.  F. 

or,  the  cosine  of  the  angle  of 

lag  is  equal  to  the  ratio  of  the  power  E.  M.  F.  to  the  impressed 
E.  M.  F.  This  may  be  otherwise  expressed  by  saying  that  if  the 
impressed  E.  M.  F.  be  multiplied  by  the  cosine  of  the  angle  of  lag, 
the  result  is  the  E.  M.  F.  required  to  overcome  the  ohmic  resist- 
ance, i.  e.,  the  power  E.  M.  F. 

621.  Choke  Coils. — The  maximum  value  of  an  alternating 
current  in  a  circuit  containing  resistance  and  inductance  is  shown 
in  the  preceding  paragraph  to  be 

T  Em 


If  R,  the  resistance  of  the  circuit,  be  small,  its  value  may  be 
negligible  as  compared  to  that  of  27T/L,  the  reactance,  and  there- 
fore the  current  may  depend  more  upon  the  reactance  of  the  cir- 
cuit than  upon  its  resistance. 

The  reactance  varies  directly  with  the  inductance  and  the 
frequency.  The  inductance  varies  with  the  geometric  arrange- 
ment of  the  circuit  and  the  proximity  of  magnetic  bodies.  The 
frequency  in  currents  for  commercial  purposes  ranges  from  25  to 
130.  If  the  current  is  to  be  employed  for  electric  lighting,  the 
frequency  should  not  fall  below  50,  otherwise  there  will  be  a  per- 
ceptible vibration  or  flicker  in  the  lamps. 

It  is  possible  to  place  in  an  alternating  current  circuit  a  coil  of 
large  wire,  and  hence  a  small  resistance,  with  a  soft  iron  core 
whose  position  may  be  varied  at  will.  As  the  core  is  inserted  in 
the  coil,  the  reactance  is  increased  and  the  current  through  the 
coil  is  cut  down;  as  the  core  is  withdrawn,  the  reactance  is  de- 
creased and  a  greater  current  passes  through. 


502  ELEMENTS  OF  ELECTRICITY. 

Such  an  arrangement  is  called  a  reactance  coil  or  a  choke  coil 
and  is  frequently  used  for  such  purposes  as  regulating  the  bril- 
liancy of  the  lights  in  a  theatre,  or  for  controlling  the  current 
applied  through  a  starting  box  to  an  alternating  current  motor. 
It  possesses  the  great  advantage  over  rheostat  control  in  that  it 
diminishes  a  current  by  setting  up  an  opposing  E.  M.  F.  and  hence 
without  loss  of  energy,  while,  in  the  case  of  the  rheostat,  power 
is  reduced  by  frittering  away  a  portion  in  heat  which  waste  must 
be  paid  for  by  the  consumer. 

1  622.  Explanation  of  Operation  of  Choke  Coil. — If  a  more  physi- 
cal conception  of  the  operation  of  a  choke  coil  be  desired,  it  may 
perhaps  be  obtained  from  the  following.  In  Par.  436  it  was  shown 
how  induction  retards  the  growth  of  a  current.  It  could  have  been 
shown  in  a  similar  manner  that  inductance  also  retards  the  decay 
of  a  current,  a  dying  current  being  represented  by  a  logarithmic 
curve  also  whose  ordinates  are  complementary  to  those  of  the 
curve  representing  the  growing  current.  Fig.  207  shows  that  under 
the  conditions  given,  the  -current  in  the  circuit  whose  inductance 
was  one  henry  required,  after  the  E.  M.  F.  was  impressed,  about 
one  second  to  reach  the  value  of  six  amperes.  Suppose  this  to 
have  been  an  alternating  current  of  a  frequency  of  50.  In  one- two- 
hundredth  of  a  second  after  the  current  started  to  rise,  or  when  it 
had  reached  a  value  of  about  .03  ampere,  the  E.  M.  F.  would  be 
reversed  and  the  current  would  be  beaten  back.  It  would  die 
down  as  slowly  as  it  rose  and  would  then  start  to  rise  in  the  op- 
posite direction  but  in  one-hundredth  of  a  second  after  it  had  been 
beaten  down  it  would  encounter  a  reversed  E.  M.  F.  and  would 
be  checked  and  driven  back,  and  so  on,  or,  figuratively,  it  would 
be  a  shuttle  cock  at  the  mercy  of  the  alternating  E.  M.  F.s.  We 
thus  see  that  inductance  makes  the  changes  in  the  current  slug- 
gish and  that  increase  of  frequency  causes  the  rising  current  to 
be  driven  back  more  promptly. 

623.  Inductance  and  Resistance  in  Series. — The  fact  that  in 
alternating  current  circuits  containing  inductance  and  resistance 
alone  the  current  always  lags  behind  the  impressed  E.  M.  F.  (Par. 
617)  affords  an  explanation  of  some  of  the  peculiarities  of  alternat- 
ing currents  to  which  reference  was  made  in  Par.  607.  As  an 
illustration,  Fig.  326  represents  a  switch  A  by  which  an  alternat- 
ing E.  M.  F.  may  be  thrown  upon  a  circuit  including  in  series  a 


ELECTRO-MECHANICS. 


503 


coil  BC  with  an  iron  core,  and  therefore  of  considerable  inductance, 
and  a  rheostat  whose  resistance  is  assumed  to  be  non-inductive, 
or  purely  ohmic.  Suppose  the  switch  to  be  closed  and  that  with 
a  voltmeter  we  read  first  the  drop  across  the  inductance  BC,  then 
the  drop  across  the  resistance  DE,  and  finally  the  total  drop 
between  B  and  E.  This  total  drop  will  be  found  to  be  less  than 
the  sum  of  the  partial  drops.  The  explanation  is  that  the  volt- 
meter takes  no  account  of  phase  but  indicates  the  virtual  volts 


RHEOSTAT 


Fig.  326. 


between  its  terminals  as  if  the  E.  M.  F.  remained  constantly  at 
this  value.  The  current  through  the  circuit  at  any  one  instant 
is  of  course  the  same  at  every  point,  but  while  it  is  in  phase  with 
the  E.  M.  F.  across  DE,  it  lags  90°  behind  the  E.  M.  F.  across  BC. 
The  maximum  E.  M.  F.  across  BC  occurs  therefore  one-quarter 
of  a  period  in  advance  of  the  maximum  E.  M.  F.  across  DE.  The 
total  drop  is  therefore  not  the  sum  of  the  partial  drops,  since  the 
maximum  values  of  these  do  not  occur  simultaneously,  but  is 
represented  by  the  hypothenuse  of  a  right  triangle  whose  remain- 
ing sides  are  the  partial  drops. 

624.  Inductance  and  Resistance  in  Parallel.— Fig.  327  repre- 
sents an  inductive  resistance  BC  and  a  non-inductive  resistance 


^W^ 


Fig.  327. 

DE  connected  in  parallel  in  an  alternating  current  circuit.    A,  F 
and  G  are  ammeters  arranged  to  read  the  currents  in  the  main 


504  ELEMENTS  OF  ELECTRICITY. 

circuit  and  in  the  branches  of  the  divided  circuit  respectively. 
It  will  be  found  that  the  sum  of  the  currents  indicated  by  F  and  G 
is  greater  than  the  current  indicated  by  A.  This  happens  because, 
as  explained  in  the  preceding  paragraph,  the  ammeters  take  no 
heed  of  phase  but  indicate  the  virtual  values  of  the  separate  cur- 
rents as  if  these  currents  were  constant,  or  as  if  their  maxima 
occurred  simultaneously.  The  drop  over  the  two  branches  is 
always  the  same,  being  the  difference  of  potential  between  M  and 
N,  but  the  current  through  DE  is  in  phase  with  this  E.  M.  F. 
while  the  current  through  EC  lags  90°.  When  the  current  through 
DE  is  a  maximum,  the  current  through  EC  is  still  one-quarter 
period  removed  from  its  maximum  and  is  correctly  the  difference 
between  the  current  through  A  and  that  through  G.  The  am- 
meter F,  however,  indicates  the  virtual  value  of  the  current 
through  EC,  as  if  the  current  were  constantly  of  this  strength. 
The  currents  through  F  and  G  are  in  quadrature  and  therefore 
the  total  current  is  represented  by  the  hypothenuse  of  a  right 
triangle  whose  remaining  sides  are  the  currents  as  indicated  by 
F  and  G. 

From  the  foregoing  we  see  that  the  current  through  resistance 
and  reactance  in  series  is  the  same  at  every  point,  but  the  voltage 
across  the  combination  is  the  vectorial  resultant  of  the  separate 
drops  as  given  by  a  voltmeter.  On  the  other  hand,  the  voltage 
across  resistance  and  reactance  in  parallel  is  the  same  over  each, 
but  the  total  current  is  the  vectorial  resultant  of  the  separate 
currents  as  given  by  an  ammeter. 

625.  Capacity. — The  subject  of  capacity  was  discussed  in 
Chapter  10  and  it  was  there  shown  that  the  capacity  of  a  con- 
denser is  not  measured  by  the  quantity  of  electricity  which  it 
can  contain  but  by  the  quantity  which  must  be  imparted  to  it 
in  order  to  raise  its  potential  unity. 

If  two  points  between  which  there  exists  a  difference  of  poten- 
tial be  connected  by  a  conductor,  there  will  be  produced  a  current 
which  will  vary  directly  with  this  difference  of  potential  and  which 
will  continue  to  flow  so  long  as  a  difference  exists.  If,  therefore, 
a  source  of  E.  M.  F.  be  connected  to  the  terminal  of  a  condenser, 
a  current  will  flow  into  the  condenser  so  long  as  the  potential  of 
the  source  is  higher  than  that  of  the  condenser.  This  current, 
however,  will  not  be  of  constant  strength,  for  as  the  condenser 
becomes  charged  its  potential  rises,  hence  the  difference  of  poten- 


ELECTRO-MECHANICS. 


505 


tial  between  it  and  the  source  grows  smaller,  and  it  is  to  this 
difference  of  potential  that  the  current  is  proportional.  We  may 
regard  the  potential  of  the  condenser  as  a  counter  E.  M.  F.  which 
opposes  the  charging  E.  M.  F.  and  thereby  diminishes  the  current. 


Fig.  328. 

As  an  analogy,  Fig.  328  represents  a  large  tank  A  of  water  of 
unvarying  head  connected  through  a  pipe  closed  by  a  stop  cock 
to  the  smaller  tank  B.  The  difference  of  the  level  of  the  water  in 
A  and  B  determines  whether  there  shall  be  a  flow  when  the  stop 
cock  is  opened.  If  at  first  B  be  empty,  the  flow  is  urged  by  the 
full  head  of  water  in  A  and  the  current  is  a  maximum.  When, 
however,  B  has  been  partly  filled,  as  shown  in  the  figure,  its  head 
is  opposed  to  that  of  the  water  in  A  and  the  flow  is  determined 
by  the  diminishing  difference  in  level  e;  therefore,  as  B  fills  up, 
the  current  dwindles  to  zero. 

626.  A  Condenser  in  an  Alternating  Current  Circuit. — Suppose 
a  condenser  to  be  connected  in  series  in  an  alternating  current 
circuit,  as  shown  in  Fig.  329.  So  long  as  the  potential  of  the  brush 


Fig.  329. 

A  is  higher  than  that  of  the  terminal  B,  a  current  will  flow  into 
the  condenser,  and  when  the  potential  of  A  is  a  maximum,  the 
condenser  will  contain  a  charge  Q,  the  maximum  under  the  given 
conditions.  As  the  potential  of  A  diminishes,  Q  flows  out  and 
B  is  entirely  discharged  when  the  potential  of  A  is  zero.  As  the 


506  ELEMENTS  OF  ELECTRICITY. 

potential  of  A  continues  to  sink  to  a  negative  maximum,  a  charge 
Q  flows  into  the  coating  D  of  the  condenser  and  finally  flows  out 
again  as  the  potential  of  A  returns  to  zero.  It  is  thus  seen  that 
although  the  circuit  is  broken  at  the  condenser,  a  charge  Q  flows 
through  the  circuit  four  times  in  each  cycle.  If  the  capacity  of 
the  condenser  and  the  frequency  be  sufficiently  great,  an  incan- 
descent lamp,  connected  as  shown,  may  be  made  to  glow  by  this 
oscillating  charge. 

627.  E.  M.  F.  and  Current  Curves  in  Case  of  Capacity.— The 

foregoing  may  be  shown  graphically  as  follows.  The  sine  curve 
EMFGH,  Fig.  330,  represents  the  impressed  E.  M.  F.,  or  the 
potential  of  the  brush  A.  The  current  from  A  to  the  condenser 
B  is  determined  by  the  difference  of  potential  between  A  and  B 
and  is  a  maximum  when  the  potential  A  is  increasing  most  rapidly. 
This  maximum  rate  of  increase  occurs  at  M  when  the  potential 
of  A  is  zero.  It  is  here  that  the  tangent  to  the  curve  is  steepest 
or  the  curve  climbs  up  most  rapidly.  The  current  therefore, 
represented  by  the  curve  JKLNO,  reaches  a  maximum  value 
MKat  this  point.  When  the  potential  of  A  reaches  its  maximum 
at  L,  the  condenser  is  fully  charged  and  the  current  no  longer 
flows  into  it.  At  this  point  the  current  curve  is  at  zero.  As 


the  potential  of  A  falls,  the  condenser  discharges,  or  the  cur- 
rent is  now  negative.  As  before,  the  negative  current  is  a  maxi- 
mum when  the  potential  of  A  is  falling  most  rapidly,  and  this  is 
the  case  at  G  where  the  potential  of  A  is  again  zero.  Finally, 
the  current  is  again  zero  at  0  where  the  potential  of  A  is  a  negative 
maximum.  It  is  thus  seen  that  in  the  case  of  capacity,  the  cur- 
rent curve  leads  the  E.  M.  F.  curve  and  is  in  quadrature  with  it. 


ELECTRO-MECHANICS.  507 

628.  Capacity   Reactance.  —  The   instantaneous  value   of  the 
E.  M.  F.  in  an  alternating  current  circuit  is 

E  =  Em  .  sin  at 

If  this  circuit  contains  capacity  alone,  the  current  leads  the 
E.  M.  F.  by  90°  and  is  given  by 

/  =  Im  •  COS  co£ 

The  instantaneous  value  of  the  power  developed  is  (Par.  494) 

IE  =  ImEm.  sin  u>t  .  cos  coZ 
The  work  done  in  a  time  dt  is 

dw  =  ImEm  .  sin  at  .  cos  wt  .  dt 

Since  the  condenser  is  charged  in  one-fourth  of  a  period  (Par.  626) 
if  this  expression  be  integrated  between  the  limits  t  =  0  and 


t  =  =    -   (Par.  612),  it  will  give  the  work  expended  in 

4  \  co  /       Zco 

charging  the  condenser. 
Performing  the  integration 

IE      1 

w  =    m   m  •  5  (sin2  coO  -f  a  constant 

co         Z 

Taking  this  between  the  above  limits 


But  in  Par.  97  it  was  shown  that  the  work  spent  in  charging  a 
condenser  of  capacity  K  is 


Equating  (I)  and  (II)  and  solving  for  Em 

I 

Substituting  for  co  its  value  27r/  (Par.  617) 

Em  =  Im  * 


508  ELEMENTS  OF  ELECTRICITY. 

Whence  also,  since  Em  =  Ev^/2  and  Im  =  IvV2  (Par.  612) 

1 
Ev  =  Iv'2rfK 

Ev  and  Iv  being  the  virtual 
E.  M.  F.  and  current  respectively. 

The  factor  5-7^  *s  called  the  capacity  reactance  of  the  circuit. 


It  is  quite  analogous  to  the  inductive  reactance  discussed  in  Par. 
619.  It  is  measured  in  ohms  and  its  dimensional  formula  (Par. 
547)  shows  it  to  be  of  the  same  dimensions,  a  velocity,  as  resist- 
ance. It  is  that  factor  by  which  the  maximum  value  of  an  alter- 
nating current  in  a  circuit  containing  capacity  must  be  multiplied 
in  order  to  obtain  the  value  of  the  reactive  E.  M.  F.  due  to 
capacity. 

629.  Alternating  E.  M.  F.  in  Circuit  Containing  Resistance  and 
Capacity. — If  the  circuit  contains  both  resistance  and  capacity, 
in  order  to  drive  a  current  Im  through  it,  the  impressed  E.  M.  F. 
must  be  sufficient  to  overcome  both  the  ohmic  resistance  and  the 
capacity  reactance.  The  E.  M.  F.  to  overcome  the  ohmic  resist- 
ance is  ImR,  that  to  overcome  the  capacity  reactance  is  Im .  0  /gr> 

^TT/A 

and  these  being  in  quadrature  (Par.  627) 


whence 


an  expression  analogous  to 

the  one  deduced  in  Par.  620,  the  denominator  being  the  impedance. 
It  will  be  noted  that  inductive  reactance  varies  directly  with 
the  frequency  /,  while  capacity  reactance  varies  inversely  with 
this  factor.  Changes  in  the  frequency  therefore  produce  diametri- 
cally opposite  results  in  the  reactances.  As  the  frequency  increases, 
the  current  through  an  inductive  circuit  decreases  while  that 
through  a  capacity  increases.  On  the  other  hand,  as  the  frequency 
decreases,  the  current  through  an  inductive  circuit  increases  and 
that  through  a  capacity  decreases. 


ELECTRO-MECHANICS.  509 

630.  Alternating  E.  M.  F.  in  Circuit  Containing  Resistance, 
Inductance  and  Capacity.  —  In  the  most  general  case,  in  order  to 
drive  a  current  Im  through  an  alternating  current  circuit  contain- 
ing resistance,  inductance  and  capacity,  the  impressed  E.  M.  F. 
must  be  sufficient  to  overcome  the  ohmic  resistance  and  the  com- 
bined reactance  of  the  inductance  and  capacity.  It  has  been  shown 
(Par.  617)  that  in  the  case  of  inductance  the  current  lags  90°;  on 
the  other  hand,  in  the  case  of  capacity  (Par.  627)  the  current 
leads  by  90°.  The  E.  M.  F.s  to  overcome  these  separate  react- 
ances therefore  differ  in  phase  by  180°  and  are  combined  by  simple 
subtraction,  hence  the  resultant  reactance  is 


and  the  most  general  ex- 
pression for  the  current  is 


631.  Electric  Resonance. — Fig.  331  represents  an  alternating 
current  circuit  in  which  there  are  connected  in  series  a  coil  of 
resistance  R  and  inductance  L  and  a  condenser  of  capacity  K. 


Fig.  331. 

From  the  preceding  paragraph,  the  current  through  the  combina- 
tion is 

E 


If  in  this  expression  we  assign  a  regular  series  of  values  to  /,  the 
frequency,  the  remaining  factors  being  kept  constant,  and  plot 
the  corresponding  values  of  the  current,  it  will  be  seen  that  at  a 
certain  value  of  /,  which  may  be  called  the  critical  frequency,  the 


510 


ELEMENTS  OF  ELECTRICITY. 


current  jumps  abruptly  to  a  maximum.     Inspection-  will  show 
that  this  maximum  is  reached  when  2w/L  =          ,  in  which  case 

the  above  expression  reduces  to  Ohm's  law.     In  this  case  also 

i  

/  =  - — Tf^'  an(*  the  periodic  time=  !//=  2wVLK  seconds.    The 

above  is  shown  in  Fig.  332,  the  curve  representing  the  values  for 

60 
50 
40 


«n 
ui 
a:  30 


*0 


30        40         .50        60 
FREQUENCY 


70 


80        90       JOO 


Fig.  332. 


different  frequencies  of  the  current  in  a  circuit  in  which  E=  110 
w  volts,  jR  =  2  ohms,  L  =  0.5  henry  and  K=  25  microfarads.  At  a 
frequency  of  about  45,  the  current  mounts  suddenly  to  55  amperes, 
while  at  a  frequency  of  5  more  or  5  less  it  is  but  little  greater  than 
three  amperes. 

If  a  heavy  pendulum  be  given  a  series  of  slight  impulses,  no 
especial  effect  will  be  produced  unless  these  impulses  be  timed 
at  the  natural  period  of  vibration  of  the  pendulum,  in  which  case 
their  effect  is  cumulative  and  it  may  be  made  to  swing  through  a 
wide  arc. 

Again,  if  various  tuning  forks  be  caused  to  vibrate  near  the  open 
end  of  a  closed  organ  pipe,  no  effect  will  be  produced  until  a  fork 
is  used  whose  period  of  vibration  corresponds  to  the  natural  period 
of  vibration  of  the  column  of  air  within  the  pipe,  and  when  this 
happens  the  column  of  air  will  vibrate  in  unison  with  the  fork  and 
the  total  volume  of  sound  emitted  will  be  greatly  increased.  This 
phenomenon  is  called  resonance. 

In  the  case  of  the  alternating  current  circuit  under  considera- 
tion, the  E.  M.  F.  is  not  applied  steadily  but  in  a  series  of  impulses 


ELECTRO-MECHANICS.  51  1 

following  each  other  at  regular  intervals.  These  impulses  produce 
no  very  marked  effect  until  the  critical  frequency  is  reached,  at 
which  time  the  current  rises  abruptly  to  its  maximum  value. 
From  analogy,  the  circuit  is  now  said  to  possess  electric  resonance. 
Resonance  exists  in  an  alternating  current  circuit  whenever 

27r/L=    —>  °r  when  the  inductive  reactance  is  exactly  counter- 


balanced by  the  capacity  reactance. 

632.  Resonance  with  Inductance  and  Capacity  in   Series.  — 

When  resonance  exists  in  a  circuit  containing  inductance  and 
capacity  in  series  (Fig.  331),  the  current  follows  Ohm's  law  and  the 
impressed  E.  M.  F.  is  simply  the  IR  drop.  The  fact,  however, 
that  the  inductive  and  the  capacity  reactances  neutralize  each 
other,  or  that  their  sum  is  zero,  does  not  mean  that  they  are 
separately  zero.  On  the  contrary,  the  difference  of  potential  across 
the  terminals  of  the  inductance  is  J.27T/L  (Par.  619)  and  that 

across  the  terminals  of  the  condenser  is  /  .  0  fv  (Par.  628)  and 


these  may  very  greatly  exceed  the  impressed  E.  M.  F.  For  ex- 
ample, in  the  numerical  example  given  in  the  preceding  paragraph, 
while  the  impressed  E.  M.  F.  is  110  volts,  the  drops  across  the 
terminals  of  the  inductance  and  of  the  condenser  are  each  7778 
volts. 

633.  Resonance  with  Inductance  and  Capacity  in  Parallel.  —  A 

particular  case  of  resonance  is  where  the  inductance  and  capacity 
are  in  parallel  as  shown  in  Fig.  333.  The  current  on  arriving  at  A 


Fig.  333. 

divides,  but  in  the  branch  L  it  is  retarded  while  in  the  branch  K 
it  is  advanced  an  equal  amount.  The  result  is  that  the  loop 
AKBL  acts  as  a  short  circuit,  the  current  surging  around  it  in 
one  direction  during  one-half  of  a  period  and  in  the  other  direction 
during  the  remaining  half.  Although  the  current  in  the  main  cir- 
cuit may  be  small,  that  in  this  loop  may  be  very  large.  This  can 
be  shown  graphically,  for  the  current  in  the  main  circuit  is  the 
resultant  of  the  currents  in  L  and  K  (Par.  624),  that  is,  it  is  the 


512  ELEMENTS  OF  ELECTRICITY. 

diagonal  of  a  parallelogram  whose  adjacent  sides  made  with  each 
other  an  angle  of  very  nearly  180°. 

634.  Power  in  an  Alternating  Current  Circuit. — In  an  alternat- 
ing current  circuit  the  instantaneous  value  of  the  power  is  the 
product  of  the  corresponding  simultaneous  instantaneous  values 
of  the  E.  M.  F.  and  the  current  (Par.  494).  Two  cases  may  arise: 
(a)  the  E.  M.  F.  and  current  may  be  in  phase,  or,  (b)  they  may 
differ  in  phase. 

If  the  E.  M.  F.  and  current  are  in  phase,  at  any  one  instant 
they  are  either  both  positive  or  both  negative  and  therefore  their 
product,  the  power,  is  always  positive.  This  is  shown  in  Fig.  334 


Fig.  334. 

in  which  the  broken  curve  representing  the  instantaneous  values 
of  the  power  lies  always  above  the  horizontal  axis.  The  power 
curve  is  seen  to  be  periodic  and  of  twice  the  frequency  of  the 
E.  M.  F.  and  current  curves.  Since  its  ordinates  represent  rate 
of  doing  work  and  its  abscissae  represent  time  (Par.  608),  the 
area  included  between  the  curve  and  the  horizontal  axis  represents 
work  performed  by  the  current.  The  work  is  positive,  for  whether 
the  current  flow  in  or  out  it  performs  work  in  overcoming  the 
resistance  of  the  circuit. 

If  the  E.  M.  F.  and  current  differ  in  phase,  their  simultaneous 
values  must  at  times  differ  in  sign  and  at  these  times  their  product, 
the  power,  must  be  negative.  The  power  curve,  therefore,  as 


ELECTRO-MECHANICS. 


513 


shown  in  Fig.  335,  extends  below  the  horizontal  axis.  The  areas 
of  the  loops  below  this  axis  represent  negative  work,  or  energy 
imparted  to  the  field  about  the  circuit  and  restored  by  this  field 
to  the  system  (Par.  616). 


Fig.  335. 

635.  Power  Factor. — In  Par.  613  it  was  shown  that  the  work 
done  by  an  alternating  current  in  one  cycle  is  £  I2mRt,  Im  being 
the  maximum  value  of  the  current,  R  the  resistance  of  the  cir- 
cuit and  t  the  time  of  one  cycle.  By  dividing  this  by  t  we  get  the 
average  rate  of  doing  work,  in  other  words,  the  average  power, 
hence 


which  may  be  written 


p=i 


watts 


W2/ 

In  the  same  paragraph  it  was  shown  that  Iv,  the  virtual  current, 
is  equal  to  Im/V2,  hence 

P_    j2  r>          T        7   r> 
—       1  y/l       ±  V    •     J-   V-ft 

But  IVR  is  that  component  of  the  virtual  E.  M.  F.  which  is  in 
phase  with  the  current,  hence  (Par.  620) 

IvR  —  Ev  .  COS  0 

hence 

P  =  IvEv .  cos  0  watts 

or  the  average  power  in 
an  alternating  current  circuit  is  equal  to  the  product  of  the  virtual 


514  ELEMENTS  OF  ELECTRICITY. 

current,  the  virtual  E.  M.  F.,  and  the  cosine  of  the  angle  of  lag  (or 
lead). 

The  power  in  an  alternating  current  circuit  must  be  read  by  a 
wattmeter,  for,  except  when  the  E.  M.  F.  and  current  are  in  phase, 
it  can  not  be  determined  by  taking  simultaneous  measurements 
with  an  ammeter  and  a  voltmeter  and  multiplying  these  readings 
together.  The  product  of  these  readings,  IVEV,  is  called  the 
apparent  power,  and  cos  </>  is  called  the  power  factor,  since,  as  shown 
above,  it  is  that  factor  by  which  the  apparent  power  must  be 
multiplied  in  order  to  obtain  the  true  power. 

If  <f>  becomes  90°,  that  is,  if  there  is  no  resistance  in  the  circuit 
so  that  the  E.  M.  F.  and  current  are  in  quadrature,  cos  0  =  0  and 
the  power  as  given  above  reduces  to  zero.  In  this  case,  the  area 
of  the  negative  loops  of  the  power  curve  (Fig.  335)  equals  that  of 
the  positive  loops. 


ELECTRO-MECHANICS.  515 


CHAPTER  44. 

ALTERNATING   CURRENT   GENERATORS. 

636.  Alternators. — The  fundamental  principles  of  alternating 
current  generators  have  already  been  brought  out  in  the  chapter 
treating  of  direct  current  generators.     It  was  there  shown  that 
the  currents  generated  in  the  revolving  armatures  described  were 
all  alternating  and  to  rectify  them  an  especial  contrivance,  the 
commutator,  was  required.    It  would  therefore  seem  that  should 
the  commutator  be  discarded  and  collector  rings  (Par.  553)  be 
substituted  in  its  place,  we  would  obtain  an  alternating  current 
generator,  or,  as  it  is  more  briefly  named,  an  alternator.    However, 
we  also  saw  that  in  the  D.  C.  generators  the  fields  were  self- 
excited,  the  direct  current  for  this  purpose  being  drawn  from  the 
commutator.     The  discarding  of  the  commutator  therefore  in- 
volves a  change  in  the  methods  of  exciting  the  field  coils,  and  for 
this  and  for  other  reasons  it  is  necessary  to  consider  these  machines 
a  little  more  in  detail. 

637.  Field  Excitation  of  Alternators. — In  most  alternators  the 
field  coils  are  excited  by  a  current  drawn  from  a  separate  source, 
such  as  from  a  battery  or  from  a  small  D.  C.  generator.    This 
auxiliary  generator,  the  exciter,  may  be  operated  in  a  number  of 
ways,    (a)  It  may  be  entirely  independent,    (b)  It  may  be  driven 
by  a  belt  from  a  pulley  on  the  shaft  of  the  alternator,    (c)  It  may 
be  mounted  upon  an  extension  of  this  shaft,    (d)  It  may  form  an 
integral  part  of  the  armature  of  the  alternator  itself.    In  this  case 
the  armature  must  be  provided  with  both  collector  rings  and 
commutator,  the  field  current  being  drawn  from  the  latter. 

638.  Compound  Alternators. — As  the  current  through  an  alter- 
nator increases,  the  internal  drop  also  increases  and  consequently 
the  ^voltage  across  the  brushes  diminishes.    We  have  seen  (Par. 
511)  how  important  it  is  in  the  case  of  electric  lighting  (for  which 
alternating  currents  are  largely  used)  that  the  voltage  delivered 
to  the  lamps  should  be  constant.    To  secure  this  constancy  of 
potential,  the  voltage  across  the  brushes  must  not  only  not  fall 


516  ELEMENTS  OF  ELECTRICITY. 

with  increase  of  current  but  must  actually  rise.  In  direct  current 
generators  this  is  secured  by  compounding  (Par.  588).  This 
remedy  is  not  directly  applicable  to  alternators  but  there  are 
several  ways  in  which  an  approximation  to  it  may  be  obtained. 
One  of  these  is  shown  diagrammatically  in  Fig.  336  which  repre- 
sents the  armature  of  an  eight-pole  alternator.  The  current 
leaving  the  armature  windings  at  the  coil  A,  before  reaching  the 
corresponding  collector  ring  passes  through  the  primary  of  a  step 
down  transformer  B.  The  core  of  this  transformer  is  attached 
to  the  armature  spider  or  forms  a  part  of  it  and  therefore  rotates 


SERIES   FIELD  COIL5 
Fig.  336. 

with  the  armature.  The  current  from  the  secondary  is  taken  to 
a  commutator  CD  which  is  mounted  upon  the  armature  shaft 
close  to  the  collector  rings  but  which,  for  the  sake  of  clearness,  is 
represented  in  the  diagram  as  moved  off  to  the  right  and  turned 
sidewise  to  the  observer.  This  commutator  has  only  as  many 
segments  as  the  alternator  has  poles,  and  the  alternate  segments 
are  connected  together  as  shown.  Brushes  pressing  against  it 
deliver  a  rectified  current  to  the  series  field  coils.  An  increase 
in  the  current  in  the  external  circuit,  and  hence  in  the  primary  of 
the  transformer,  causes  an  increase  in  the  current  through  the 
secondary,  and  hence  through  the  field  coils,  which  in  turn  causes 
the  desired  rise  in  voltage. 

It  is  sometimes  possible  to  dispense  with  the  transformer  and 
to  take  the  current  direct  from  the  coil  A  to  the  commutator. 
As  a  rule,  however,  alternators  generate  a  high  voltage  current 
which,  besides  being  dangerous,  is  apt  to  cause  excessive  sparking 


ELECTRO-MECHANICS.  517 

at  the  commutator.    For  these  reasons  the  transformer  is  to  be 
preferred. 

639.  Alternators  Usually  Multipolar. — It  is  in  general  necessary 
that  an  alternator  should  be  multipolar.    This  will  be  seen  from 
the  following.    A  small  alternator  may  be  driven  at  1800  revolu- 
tions per  minute.    This  speed  may  be  exceeded  by  some  of  the 
turbine  driven  machines  but  is  near  the  limit  for  the  average 
small  generator  and  much  above  the  limit  for  large  machines.    At 
this  rate,  a  point  on  the  circumference  of  a  twelve  inch  armature 
is  travelling  faster  than  a  mile  per  minute.    But  at  1800  revolu- 
tions per  minute  the  frequency  of  the  current  from  a  bipolar 
machine  is  only  30.    This,  we  have  seen  (Par.  621),  is  too  low  for 
the  operation  of  an  incandescent  lamp.    Moreover,  frequencies 
as  high  as  120  are  often  required.    Since  the  speed  of  the  alter- 
nator can  not  be  increased,  such  frequencies  can  be  obtained 
only  by  increasing  the  number  of  poles.    In  some  of  the  larger 
modern  alternators,  the  number  of  poles  has  approached  one 
hundred. 

640.  Classes  of  Alternators. — As  shown  above,  the  classifi- 
cation of  D.  C.  generators  according  to  the  method  of  field  excita- 
tion into  series,  shunt  and  compound  machines  is  not  applicable 
to  alternators.    They  may,  however,  be  divided  into  two  general 
classes;  (a)  those  with  stationary  field  'and  revolving  armature, 
and  (b)  those  with  stationary  armature  and  revolving  field.    Of 
this  second  class  there  is  a  subdivision,  the  inductor  alternator, 
in  which,  although  the  field  revolves,  the  exciting  current  passes 
through  a  single  coil  which  is  stationary  (Par.  643).    From  an 
electrical  standpoint,  there  is  no  call  for  these  divisions,  the 
principle  being  the  same  in  all,  but  each  possesses  certain  minor 
advantages  and  it  is  therefore  desirable  to  consider  them  separately 
though  briefly. 

It  will  shortly  be  shown  that  alternators  may  be  designed  to 
deliver  a  single  current  or  two  or  more  separate  and  distinct 
currents  which  differ  in  phase  and  accordingly  they  are  also 
classed  as  single  phase  or  as  polyphase. 

641.  Alternators    with    Revolving    Armatures. — The   simplest 
form  of  alternator  with  revolving  armature  is  figured  and  ex- 
plained in  Par.  553.    The  majority  are  multipolar.    A  diagram- 


518 


ELEMENTS  OF  ELECTRICITY. 


matic  end  view  of  such  a  machine  is  given  in  Fig.  337,  and  in  Fig. 
338  a  similar  four-pole  machine  is  shown  as  rectified,  that  is,  the 
field,  the  armature  and  the  collector  rings  are  represented  as 
having  been  straightened  out.  With  clockwise  rotation,  the  coils 


O 


FIELD 

CURRENT 


Fig.  337. 

A,  B,  C,  D  move  from  left  to  right  as  indicated  by  the  large 
arrow.  Application  of  the  rule  given  in  Par.  421  shows  that  at 
the  instant  represented  a  clockwise  E.  M.  F.  is  induced  in  A  and 
in  C  and  a  counter-clockwise  E.  M.  F.  in  B  and  in  D,  but  since 


000 


Fig.  338. 

these  coils  alternate  in  the  direction  of  their  winding,  they  add 
their  respective  E.  M.  F.s.  The  current  passes  into  the  external 
circuit  from  the  collector  ring  EE  through  the  brush  G  and  returns 
through  the  brush  H  which  is  in  contact  with  the  ring  FF.  The 
direction  of  this  current  is  reversed  as  A  passes  beneath  the  center 
of  S. 


ELECTRO-MECHANICS. 


519 


642.  Alternators  with  Revolving  Field. — In  alternators  with 
revolving  field,  the  field  may  retain  its  relative  position  exterior 
to  the  armature,  but  far  more  frequently  they  interchange  places 
and  the  revolving  field  is  internal.  Roughly  speaking,  the  field 
core  resembles  the  hub  of  a  wheel  whose  spokes  have  all  been 
sawed  off  to  a  length  of  two  or  three  inches.  The  field  coils  are 
wrapped  about  these  spokes,  alternating  in  direction  so  as  to 
obtain  the  desired  polarity.  The  exciting  current  is  brought  in 
and  taken  out  by  means  of  a  pair  of  slip  rings  (identical  in  opera- 
tion with  collector  rings).  Fig.  337  would  represent  such  a  ma- 
chine if  the  field  circuit  and  the  external  circuit  were  interchanged, 


Fig.  339. 

that  is,  if  the  exciting  direct  current  were  brought  in  through  the 
collector  rings  and  if  the  present  field  circuit  were  used  as  the 
external  circuit.  The  armature,  Fig.  339,  is  built  up  of  laminated 
punchings,  spaces  being  left  for  ventilation.  The  coils  are  placed 
in  slots  and  held  in  position  by  wedges. 

The  great  advantage  of  this  form  of  alternator  is  that  the  cur- 
rent, which  we  have  seen  is  usually  of  high  voltage,  is  taken  off 
through  fixed  connections,  which  may  be  insulated  to  any  desired 
degree,  and  only  the  relatively  small  exciting  current  passes 
through  the  sliding  contacts  on  the  slip  rings. 


520 


ELEMENTS  OF  ELECTRICITY. 


643.  The  Inductor  Alternator. — The  inductor  alternator,  shown 
diagrammatically  in  section  in  Fig.  340,  possesses  the  advantage 
of  having  no  sliding  contacts  and  therefore  requires 
no  collecting  rings  or  brushes  and  is  free  from  the 
sparking  which  occurs  in  other  machines.  It  con- 
sists of  an  inductor,  a  rotating  toothed  soft-iron  disc 
around  whose  edge  there  is  a  deep  groove.  In  this 
groove  lies  the  annular  field  coil  C  which  is  fastened 
to  the  frame  work  and  therefore  does  not  rotate 
with  the  inductor.  When  a  current  flows  through 
C,  the  inductor  becomes  magnetized,  its  faces 
being  of  opposite  polarity  and  hence  the  teeth  on 
one  side  being  all  of  like  polarity.  The  frame 
work  which  surrounds  this  revolving  inductor 
has  inward  projections  corresponding  to  the  mov- 
ing poles,  and  upon  these  projections  the  armature 


Fig.  340. 


coils  are  wrapped.  Since  the  poles  on  each  side  do  not  alternate 
in  polarity,  there  is  no  reversal  of  flux  through  the  armature  coils 
but  this  flux  rises  and  falls  and  thus  produces  an  alternating  cur- 
rent in  the  coils. 

644.  Polyphase  Alternators. — Suppose  that  the  ends  of  the  two 
coils  in  Fig.  269,  instead  of  terminating  in  the  commutator  seg- 
ments as  shown,  should  each  be  connected  to  a  separate  collector 
ring  as  shown  in  Fig.  341.  There  being  no  electrical  connection 
between  these  coils,  a  pair  of  brushes  C  could  be  applied  to  the 
rings  of  the  coil  B  and  lead  current  from  this  coil  into  an  external 
circuit.  A  second  pair  of  brushes  D  could  be  applied  to  the  rings 
of  A  and  lead  current  from  A  into  an  entirely  separate  external 
circuit.  As  the  armature  rotates,  an  equal  E.  M.  F.  is  generated 
in  each  coil  but  the  currents  in  the  respective  circuits  vary  with 
the  resistances  of  these  circuits  and  are  entirely  independent  of 
each  other,  in  fact,  the  machine  is  electrically  equivalent  to  two 
separate  and  distinct  machines,  the  only  connection  between  the 
two  being  that  they  generate  equal  E.  M.  F.s  of  equal  periodicity. 
If  the  E.  M.  F.  curves  of  the  two  coils  be  plotted  on  a  common 
axis  of  time,  it  will  be  seen  that  their  maxima  occur  at  a  constant 
phase  difference  of  90°.  Since  the  machine  thus  generates  two 
distinct  currents  of  different  phases,  it  is  called  a  two-phase  or  a 
di-phase  alternator. 

Theoretically,  other  coils  could  be  inserted  midway  between 


ELECTRO-MECHANICS. 


521 


those  of  Fig.  341  and  still  others  between  these,  each  with  its  own 
collector  rings  and  each  supplying  a  separate  external  circuit  with 
current  differing  in  phase  from  the  currents  from  the  other  coils. 
Practically,  the  distinct  windings  of  such  alternators  rarely  exceed 


Fig.  341. 

three.  Those  which  generate  more  than  one  current  are  designated 
as  polyphase;  those  which  generate  but  one  are,  in  contra-distinc- 
tion,  called  single  phase. 

It  can  be  shown  that  to  generate  these  polyphase  currents  it  is 
not  necessary  that  the  windings  for  each  phase  should  be  entirely 
separate.  For  example,  as  shown  in  Fig.  342,  by  tapping  a  ring- 


Fig.  342. 

wound  armature  at  four  points  90°  apart  and  by  connecting  each 
of  the  tapping  wires  to  a  collector  ring,  we  obtain  a  two-phase 
alternator.  At  the  instant  shown  in  the  diagram  the  leads  A  are 
carrying  the  entire  current,  the  current  in  the  leads  B  being  zero 
since  the  points  to  which  their  tapping  wires  are  connected  are 


522 


ELEMENTS  OF  ELECTRICITY. 


momentarily  at  the  same  potential.  When,  however,  the  armature 
has  turned  through  an  angle  of  90°,  these  conditions  are  reversed 
and  the  leads  B  will  carry  the  entire  current,  while  the  current 
in  A  will  be  zero. 

While  polyphase  currents  are  used  to  a  limited  extent  in  a  three- 
wire  lighting  system,  their  principal  use,  as  will  be  explained  in 
the  following  chapter,  is  for  the  operation  of  alternating  current 
motors. 

645.  Tri- Phase  Alternators. — In  its  most  general  form,  the 
armature  of  a  tri-phase  alternator  carries  three  distinct  windings 
spaced  120°  apart  and  supplied  with  six  collector  rings  by  which 
currents  can  be  distributed  to  three  separate  circuits.  The  E.  M. 
F.  generated  by  such  an  alternator  is  shown  in  Fig.  343,  the  sine 
waves  being  of  equal  amplitude  but  differing  in  phase  by  120°. 

If  the  resistances  of  the  three  circuits  are  equal,  then  the  cur- 
rents are  also  equal  and  the  circuits  are  said  to  be  balanced.  In 
such  a  case  the  curves  in  Fig.  343  may  be  taken  as  representing 


Fig.  343. 

the  currents  also.  Examination  of  this  figure  will  show  that  at 
any  point  along  the  horizontal  axis,  the  sum  of  the  ordinates  is 
zero.  For  example,  at  A  and  C  where  the  current  in  one  of  the 
circuits  is  zero,  the  currents  in  the  other  two  circuits  are  both 
equal  and  opposite,  and  at  B  and  D  where  the  current  in  one  of 
the  circuits  is  a  maximum,  the  sum  of  the  currents  in  the  other 
two  circuits  is  equal  and  opposite.  It  is  therefore  possible  when 
the  circuits  are  balanced  to  discard  three  collector  rings  and  three 
lead  wires,  for  whether  the  current  goes  out  on  one  or  on  two  wires, 
an  equal  current  comes  in  on  the  remaining  wires  or  wire.  The 
arrangement  of  such  a  three-wire  three-phase  system  is  shown  in 
Fig.  344. 


ELECTRO-MECHANICS. 


523 


Should  the  circuits  not  be  balanced,  it  is  still  possible  to  reduce 
the  number  of  leads  and  collector  rings  from  six  to  four,  the  fourth 
wire  serving  as  a  common  return  for  the  excess  current  of  the 
other  three. 

646.  Tri-Phase  Delta  Connection. — In  Fig.  344,  a  represents 
diagrammatically  a  ring  wound  armature  tapped  at  three  points 
120°  apart,  each  tapping  wire  terminating  in  a  collector  ring. 
These  rings,  A,  B,  C,  for  the  sake  of  clearness  are  represented  as 


Fig.  344. 

separated  from  their  common  axis.  The  same  armature  is  repre- 
sented in  6  in  a  still  more  highly  conventionalized  form,  the  curved 
portions  between  the  tapping  wires  being  straightened  out  and 
the  rings  being  drawn  at  the  vertices  of  the  resulting  triangle. 
This  diagram  also  shows  the  three  leads  running  from  these  rings 
and  the  arrangement  of  lamps  so  as  to  produce  a  balanced  system. 
On  account  of  the  shape  of  the  diagram  this  is  called  a 
^-connection,  sometimes  also  a  mesh-grouping.  At  one  instant 
the  entire  current  flows  out  on  A  and  returns  through  the  lamps 
D  and  E;  at  another  instant  it  flows  out  on  C  and  returns 
through  D  and  F;  at  still  another  it  flows  out  on  B  and  returns 
through  E  and  F;  at  all  others,  a  varying  current  flows  through 
each  lamp. 

At  the  instant  represented  in  a,  Fig.  344,  the  armature  coils 
between  B  and  C  are  sending  current  out  by  C,  and  the  coils 
between  A  and  C  (except  the  few  to  the  left  of  the  neutral  plane) 
are  contributing  to  this  current.  The  currents  in  these  two  por- 
tions of  the  armature  windings  do  not  reach  their  maxima  simul- 
taneously but  the  total  resultant  current  is  a  maximum  when 
these  component  currents  are  equal  which  is  the  case  at  A,  the 
60°  phase  in  Fig.  343±  The  maximum  current  in  the  leads  is 
therefore  2  sin  60°  =  V3  times  the  maximum  current  in  one  portion 


524 


ELEMENTS  OF  ELECTRICITY. 


of  the  armature  windings.  The  maximum  E.  M.  F.  between  any 
two  of  the  leads  is,  however,  no  greater  than  that  in  one  portion 
of  the  armature  windings. 

647.  Tri-Phase  Y-Connection. — Suppose  that  in  addition  to 
tapping  the  ring-wound  armature  in  three  points,  as  described 
in  the  preceding  paragraph,  we  cut  the  winding  at  these  points 
and  connect  the  corresponding  ends  together  as  shown  in  Fig. 
345  a.  The  current  entering  at  B  (at  the  instant  represented  in 


Fig.  345. 

the  diagram)  flows  to  the  common  junction  at  the  center  where  it 
divides,  a  portion  going  to  A,  the  remainder  to  C.  This  arrange- 
ment, shown  still  more  diagrammatically  in  b,  is  called  a  Y-con- 
nection,  sometimes  also  a  star  grouping. 

The  E.  M.  F.  of  the  coils  between  B  and  a  is  now  in  series  with 
that  of  those  between  a  and  A  and  of  those  between  a  and  C, 
excepting  in  both  cases  the  few  turns  to  the  left  of  the  neutral 
plane.  The  maximum  E.  M.  F.  between  the  leads  of  b  is  therefore 
the  sum  of  the  E.  M.  F.s  in  two  of  the  three  portions  of  the  arma- 
ture windings  at  the  moment  when  the  E.  M.  F.  in  the  third 
portion  is  zero.  This  is  represented  by  the  double  ordinate  at  A 
in  Fig.  343.  But  A  being  at  the  60°  phase,  this  double  ordinate 
is  2  sin  60°  =  \/3,  or  the  maximum  E.  M.  F.  between  any  two  of 
the  leads  is  V3  times  the  maximum  E.  M.  F.  developed  in  a 
single  portion  of  the  armature  windings. 

On  the  other  hand,  since  at  any  one  instant  never  more  than 
two  of  the  portions  of  the  armature  windings  can  combine  in 
delivering  current,  and  since  these  two  portions  are  always  in 
series,  the  maximum  current  in  the  leads  is  the  same  as  the  maxi- 
mum current  in  any  one  of  these  portions. 

It  will  be  noted  that  in  the  A-connection  the  current  is  V3 
times  the  maximum  of  that  in  the  armature  coils,  while  in  the 


ELECTRO-MECHANICS.  525 

Y-connection  the  voltage  is  V3  times  the  maximum  of  that  in 
these  coils.  The  power,  IE,  developed  by  the  two  arrangements 
is  therefore  the  same. 

648.  Transformation  of  Direct  and  of  Alternating  Currents. — 

We  have  seen  that  the  secret  of  the  electrical  transmission  of 
power  is  the  employment  of  currents  of  high  potential  (Par.  502) . 
On  account  of  freedom  from  trouble  caused  by  sparking  at  the 
commutator,  it  is  true  as  a  general  statement  that  an  alternating 
current  can  be  turned  out  at  a  higher  voltage  than  can  a  direct 
current.  Whether  the  current  produced  by  a  generator  be  direct 
or  alternating,  it  is  often  desirable  to  raise  its  voltage  still  higher 
before  sending  it  out  on  the  line,  and  whether  this  be  done  or  not, 
it  is  almost  always  necessary  at  the  distant  end  of  the  line  to 
reduce  the  voltage  to  fit  the  standard  machines  or  lamps  with 
which  it  is  to  be  used.  In  this  transmission,  therefore,  a  current 
must  be  stepped  up  at  the  sending  station  and  stepped  down  at 
the  receiving  station. 

In  the  case  of  direct  currents,  this  transformation  is  effected  by 
motor  generators  (Par.  605).  These  machines  are  costly,  their 
operation  involves  a  considerable  loss  of  power  and  they  require 
as  much  attention  as  the  generator  itself.  If  power  is  to  be  dis- 
tributed among  scattered  buildings,  a  motor  generator  and  an 
engineer  would  be  required  in  each,  also  space  for  installation  of 
the  machine.  On  the  other  hand,  these  changes  in  alternating 
currents  are  made  by  transformers  which  are  relatively  inexpen- 
sive, require  little  or  no  attention  and  have  an  efficiency  in  some 
cases  exceeding  98  per  cent.  They  may  be  placed  wherever 
needed  and  occupy  but  little  room  since  they  are  usually  mounted 
against  a  wall  or  upon  a  pole  like  a  letter  box.  For  these  reasons, 
for  the  transmission  of  power  to  a  distance,  the  alternating  current 
has  a  great  advantage  over  the  direct. 

649.  Transformers. — The  principle  of  transformers  was  out- 
lined in  Par.  431  but  they  are  considered  here  again  in  order  that 
some  additional  facts  about  their  use  may  be  brought  out.    That 
they  rightfully  fall  under  the  heading  of  the  present  chapter,  the 
following  will  show.    An  alternator  is  a  machine  which  induces 
an  alternating  E.  M.  F.  by  rapidly  varying  the  magnetic  flux 
through  a  coil.    From  this  point  of  view,  a  transformer  is  also  an 
alternator,  the  E.  M.  F.  in  the  secondary  being  induced  by  the 


526 


ELEMENTS  OF  ELECTRICITY. 


changing  flux  produced  in  it  by  the  primary.  Moreover,  since  the 
transformer  has  no  moving  parts  (and  is  hence  sometimes  called 
static),  there  is  no  loss  of  energy  in  overcoming  friction,  etc.,  and 
by  proper  design  the  combined  losses  due  to  magnetic  leakage, 
eddy  currents,  hysteresis  and  resistance  may  be  reduced  to  less 
than  two  per  cent,  so  that  we  may  say  that  the  transformer  is  the 
most  efficient  of  machines. 

Transformers  are  of  two  types,  the  core  or  ring  transformer 
(Fig.  204)  and  the  shell  transformer  (Fig.  205).  The  shell  trans- 
former is  the  more  frequently  used  but,  for  the  sake  of  clearness, 
the  following  diagrams  represent  ring  transformers. 

In  the  actual  construction  of  the  shell  transformer,  the  coils  are 
usually  wound  in  separate  portions  which  are  thoroughly  insulated 
and  then  sandwiched  together,  after  which  they  are  placed  in  a 
form  and  the  laminated  iron  punchings  of  which  the  shell  is  com- 
posed are  built  up  around  them.  The  completed  coils  are  then 
put  in  an  iron  case  which  is  usually  filled  with  oil.  This  serves  a 
double  purpose;  it  aids  the  insulation  of  the  coils,  prevents  the 
penetration  of  moisture  into  the  wrappings  and  prevents  excessive 
heating  of  the  coils.  In  some  of  the  larger  transformers,  the  oil 
itself  is  cooled  by  water  circulating  in  pipes  which  pass  through 
the  oil.  In  others,  the  oil  is  omitted  and  cooling  is  brought  about 
by  currents  of  air  driven  over  the  coils. 

If  a  current  be  sent  through  the  primary  of  a  transformer,  it 
will  produce  in  the  core  a  certain  number  of  lines  of  force.  These 
lines,  as  shown  in  Fig.  346,  penetrate  every  turn  of  the  coils  in 


1 

\ 

, 

r- 

»                  c 

p              < 

< 

-4- 

I                 S 

A 

c 

r+H 

li_ 

1               < 

i— 

"•*- 

j                  < 

t 

*,_ 

•-<  -< 

1 
_' 

Fig.  346. 

both  primary  and  secondary.  An  equal  E.  M.  F.  is  therefore 
induced  in  every  turn.  If  this  E.  M.  F.  be  e,  and  if  there  be  Af' 
turns  in  the  primary  and  N"  in  the  secondary,  the  E.  M.  F.  in  the 
primary  is  E'=  N'e,  that  in  the  secondary  is  E"  =  N"e,  whence 

E'   :  E"=N'   :    N" 


ELECTRO-MECHANICS. 


527 


or,  as  already  shown  (Par.  431),  the  E.  M.  F.s  in  the  two  coils  are 
to  each  other  as  the  number  of  turns  in  the  respective  coils. 

650.  Operation  of  Transformer. — In  Par.  431  it  was  shown 
that  the  work  done  in  the  primary  of  a  properly  designed  trans- 
former is  equal  to  that  done  in  the  secondary.  It  follows  from 
this  principle  that  the  current  in  the  primary  varies  with  the 


Fig.  347. 

current  in  the  secondary  and  that  when  the  secondary  circuit  is 
open  there  should  be  no  current  in  the  primary.  This  can  be 
shown  experimentally  by  the  arrangement  shown  in  Fig.  347. 
With  the  switches  in  the  secondary  circuit  open,  the  ammeter  in 
the  primary  circuit  indicates  the  merest  trace  of  a  current.  Reflec- 
tion will  show  that  the  primary,  a  coil  of  small  resistance  wrapped 
about  a  soft  iron  core,  is  nothing  more  nor  less  than  a  choke  coil 
as  described  in  Par.  621,  and  that  the  current  is  cut  down  by  the 
choking  effect.  The  small  current  which  does  get  through,  the 
"no  load  current,"  is  just  sufficient  to  maintain  the  magnetic  flux. 

If  now  one  of  the  switches  in  the  secondary  be  closed,  the 
ammeter  will  indicate  a  current  through  the  primary.  If  a  second 
switch  be  closed,  the  current  through  the  primary  is  doubled ;  if  a 
third  switch  be  closed,  it  is  trebled,  in  other  words,  the  current 
through  the  primary  adjusts  itself  to  conform  to  the  current  in 
the  secondary,  or,  the  primary  acts  as  an  automatic  valve  and 
permits  only  so  much  current  to  flow  through  it  as  is  needed  to 
supply  the  demands  of  the  secondary. 

This  very  remarkable  property  may  be  explained  as  follows. 
When  an  E.  M.  F.  is  impressed  upon  the  primary,  the  secondary 
circuit  being  open  (Fig.  346),  a  current  flows  and  produces  within 
the  primary  a  magnetic  flux.  The  lines  of  force,  as  shown  by  the 
arrowheads,  travel  around  the  magnetic  circuit  and  enter  the 
primary  from  below.  This  sets  up  an  induced  E.  M.  F.  in  the 
primary  opposite  to  the  actual  E.  M.  F.  (Par.  421)  and  conse- 


528  ELEMENTS  OF  ELECTRICITY. 

quently  cuts  down  the  current  in  the  primary.  An  E.  M.  F.  is  also 
set  up  in  the  secondary  but  produces  no  current  since  this  circuit  is 
open.  When,  however,  the  secondary  circuit  is  closed,  a  current 
flows  as  indicated  by  the  arrowhead.  This  current  produces  lines 
of  force  opposite  in  direction  to  those  from  the  primary,  that  is,  it 
diminishes  the  number  of  lines  from  the  primary  (Par.  418,  6). 
This  in  turn  diminishes  the  choking  effect  and  allows  a  larger 
current  to  flow  through  the  primary. 

From  the  facts  brought  out  above  it  will  be  seen  that  in  any 
given  transformer  the  voltage  in  the  secondary  varies  directly 
with  the  voltage  in  the  primary;  on  the  other  hand,  the  current 
in  the  primary  varies  directly  with  the  current  in  the  secondary; 
in  other  words,  the  primary  determines  the  voltage;  the  secondary 
determines  the  current. 

651.  Connection  of  Transformers. — On  account  of  the  choking 
effect  described  in  the  preceding  paragraph,  transformers  are  not 
connected  in  series  but  in  parallel.  Fig.  348  represents  an  alter- 


Fig.  348. 

nator  delivering  high  potential  current  to  two  mains  and  through 
transformers  connected  in  parallel  distributing  energy  from  these 
mains  to  the  stations  A  and  B. 

652.  Auto-Transformers. — The  transformers  described  in  the 
preceding  paragraphs  are  used  when  the  voltage  in  the  primary 
is  to  be  very  materially  changed,  as  for  example  when  it  is  to  be 
increased  or  diminished  tenfold,  or,  as  a  minimum,  when  it  is  to 
be  doubled  or  halved.  Smaller  changes  in  voltage  may  be  made 
by  means  of  resistance,  but  this  we  have  shown  to  be  wasteful. 
A  better  method  is  to  use  the  so-called  auto-transformer,  shown 
diagrammatically  in  Fig.  349.  This  is  a  transformer  in  which  the 
primary  and  the  secondary  coils  are  combined  in  one.  In  prin- 
ciple it  does  not  differ  from  the  ordinary  transformer.  As  explained 
in  Par.  649,  when  a  current  is  sent  through  the  primary  coil,  an 
equal  E.  M.  F.  is  developed  in  every  turn.  The  E.  M.  F.  in  the 


ELECTRO-MECHANICS. 


529 


secondary  therefore  varies  directly  with  the  number  of  turns 
tapped  by  it.  In  the  diagram,  the  secondary  is  used  to  step  down 
the  voltage  in  the  primary.  If  the  current  were  delivered  to  the 


Fig.  349. 

secondary  and  drawn  from  the  primary,  the  voltage  would  be 
stepped  up. 

653.  Rectification    of    Alternating    Current. — An    alternating 
current  may  be  rectified  in  several  ways.     It  has  already  been 
shown  (Par.  556)  how  it  may  be  rectified  at  the  point  of  origin  by 
means  of  a  commutator.    It  is,  however,  frequently  desirable  to 
transmit  the  current  to  a  distance  as  alternating  and  to  rectify 
it  at  the  receiving  station.    In  this  case  it  may  be  rectified  by  (a) 
mechanical  means,  or  by  (b)  electro-chemical  means. 

An  alternating  current  is  rectified  mechanically  by  means  of  a 
synchronous  converter,  also  called  a  rotary  converter.  Briefly  ex- 
plained, this  is  a  generator  with  both  commutator  and  collector 
rings.  The  alternating  current  is  delivered  to  the  collector  rings 
and  the  machine  operates  as  a  motor.  While  so  operating,  direct 
current  is  drawn  from  the  commutator. 

Alternating  current  may  also  be  rectified  mechanically  by  a 
motor-generator  (Par.  605),  the  motor  being  driven  by  the  alter- 
nating current  and  direct  current  being  drawn  from  the  com- 
mutator of  the  generator  at  the  opposite  end  of  the  shaft. 

The  electro-chemical  rectifiers  are  of  several  kinds.  In  one,  the 
current  is  passed  through  a  cell  containing  electrodes  of  aluminum 
and  of  lead  or  steel,  the  aluminum  having  the  property  of  per- 
mitting the  current  to  pass  when  it  is  the  cathode  but  suppressing 
it  when  it  is  the  anode.  Allied  to  this  is  the  mercury  arc  rectifier 
which  will  now  be  described. 

654.  The  Mercury  Arc  Rectifier. — In  the  description  of  the 
mercury  vapor  lamp  (Par.  527),  it  was  shown  that  the  resistance 


530  ELEMENTS  OF  ELECTRICITY. 

to  the  passage  of  the  current  was  confined  mainly  to  the  surface 
of  the  negative  electrode  and  was  so  great  that  several  thousand 
volts  were  required  to  break  it  down,  but  that  once  that  it  had 
been  broken  down,  a  current  could  be  maintained  by  a  small 
voltage  provided  that  this  current  did  not  fall  below  a  certain 
minimum.  If  it  fell  below  this,  the  negative  electrode  resistance 
was  re-established  and  the  current  was  interrupted. 

This  principle  is  utilized  in  the  mercury  arc  rectifier,  an  appara- 
tus for  the  conversion  of  alternating  currents  into  the  relatively 
small  direct  currents  such  as  are  employed  in  charging  the  smaller 
storage  batteries.  It  may  be  used  with  either  single  phase  or 
polyphase  currents.  Its  operation  will  be  understood  from  the 
following.  Fig.  350  represents  diagrammatically  one  of  these 


Fig.  350. 

converters.  It  consists  of  a  pear-shaped  exhausted  glass  globe 
of  about  nine  inches  in  diameter.  Through  its  top  extend  the 
terminals  A  and  B  which  connect  on  the  interior  with  the  iron 
electrodes  C  and  D.  A  third  terminal  enters  below  and  connects 
with  the  mercury  electrode  E.  Suppose  that  desiring  to  charge 
the  storage  battery  F  by  means  of  current  from  an  alternator  M, 
we  should  make  connections  as  shown  on  the  right  of  the  diagram. 
No  current  can  flow  in  either  direction  until  the  negative  electrode 
resistance  at  either  D  or  E  be  broken  down.  Suppose  that  as 
explained  below  this  resistance  be  broken  down  at  E.  Current 
will  now  flow  through  the  circuit  in  the  direction  BDEF  but  will 
continue  to  flow  for  only  a  small  fraction  of  a  second.  As  soon 
as  the  voltage  between  D  and  E  drops  to  about  ten  volts,  the 


ELECTRO-MECHANICS. 


531 


resistance  at  E  is  re-established  and  the  current  is  interrupted. 
When  the  E.  M.  F.  reverses,  no  current  can  flow,  for  the  resistance 
at  D  has  not  yet  been  broken  down.  We  see  then  that  this  ar- 
rangement could  not  be  used.  Now  suppose  a  direct  current 
generator  G  to  be  connected  as  shown  on  the  left  of  the  diagram. 
When  the  resistance  at  E  has  once  been  broken  down,  direct 
current  from  G  will  flow  steadily  in  the  direction  ACEF.  If  now 
the  alternator  be  turned  on,  the  alternating  E.  M.  F.  in  the 
direction  BDE  can  send  a  current  through  the  circuit  because  the 
direct  current  from  G,  by  preventing  the  resistance  at  E  from 
reasserting  itself,  keeps  open  the  road  through  E,  but  the  alternate 
impulses  in  the  reverse  direction  can  send  no  current  since  the 
resistance  at  D  prevents.  It  is  thus  seen  that  by  such  an  arrange- 
ment the  alternating  current  from  one-half  of  each  cycle  could  be 
used  to  charge  the  battery. 

The  illustration  above  is  purely  hypothetical  but  is  intended 
to  bring  out  the  fact  that  if  in  any  manner  the  resistance  at  the 
negative  electrode  can  be  kept  broken  down,  than  the  apparatus 
becomes  selective  in  its  operation  and  permits  current  to  pass  in 
one  direction  but  not  in  the  other,  in  other  words,  it  becomes  a 
rectifier. 

655.  Rectification  of  Single  Phase  Current. — The  arrangement 
of  the  converter  to  rectify  a  single  phase  current  is  shown  in  Fig. 
351.  The  leads  from  the  alternator  M  terminate  in  the  electrodes 


Fig.  351. 

C  and  D,  but  at  A  and  B  branches  are  thrown  off  which  include 
the  inductance  coils  G  and  H  and  unite  at  J.  To  one  side  of  the 
electrode  E  there  is  an  auxiliary  mercury  electrode  F  which  is 


532  ELEMENTS  OF  ELECTRICITY. 

connected  through  a  resistance  R  with  the  wire  from  A  to  G. 
The  globe  is  mounted  so  that  it  may  readily  be  tilted. 

To  charge  a  storage  battery,  the  battery  is  connected  between 
E  and  J  as  shown.  The  globe  is  then  tilted  until  the  mercury  in 
E  connects  with  that  in  F.  At  this  instant  the  current  passes 
through  the  path  MARFEJHBM.  The  globe  is  now  released 
and  as  the  thread  of  mercury  between  E  and  F  is  broken,  an  arc 
is  produced,  some  of  the  mercury  is  ionized  and  the  vapor  in  the 
globe  is  thereby  rendered  a  conductor.  The  path  of  the  current 
is  now  MACEJHBM,  but  the  E.  M.  F.  acting  in  this  direction 
soon  dies  down  and  then  reverses,  that  is,  acts  in  the  direction 
MBD.  The  inductance  of  the  coil  H  now  comes  into  play  and 
prolongs  the  current  through  H,  a  momentary  current  flowing 
around  the  circuit  JHBDEJ.  Before  this  delayed  current  has 
died  down  to  the  point  where  the  resistance  of  E  is  re-established, 
it  is  picked  up  by  the  growing  E.  M.  F.  in  the  direction  MBD,  the 
circuit  now  being  MBDEJGAM.  At  the  next  reversal,  the  in- 
ductance of  the  coil  G  comes  into  play,  and  so  on,  these  induced 
delayed  currents  fulfilling  the  part  of  the  direct  current  described 
in  the  preceding  paragraph  and  keeping  the  path  through  E  open. 

656.  Comparison  of  Alternating  and  Direct  Currents. — Alter- 
nating current  generators,  since  they  require  no  commutator,  are 
somewhat  cheaper  to  construct  than  those  for  direct  current,  but 
this  may  be  counterbalanced  by  the  cost  of  the  separate  field 
exciter.  The  great  advantage  of  alternating  currents  is  the  ease 
with  which  they  may  be  transformed  and  the  simplicity  and  the 
efficiency  of  the  static  transformers  used  for  this  purpose.  On 
the  other  hand,  they  can  not  be  used  in  electrolytic  work  nor  in 
charging  storage  batteries  and  alternating  current  motors  fall 
behind  direct  current  motors  both  in  efficiency  and  in  speed 
regulation.  While  most  incandescent  lamps  operate  equally  well 
with  either  kind  of  current,  the  arc  lamp  mechanism  for  alternating 
currents  is  not  so  satisfactory  as  that  for  direct  currents.  As  a 
general  statement  therefore,  alternating  current  is  most  suitable 
where  power  is  to  be  transmitted  to  a  distance;  in  all  other  cases 
direct  current  is  to  be  preferred. 


ELECTRO-MECHANICS.  533 


CHAPTER  45. 

ALTERNATING   CURRENT   MOTORS. 

657.  Alternating   Current  Motors. — The  electrical  conditions 
encountered  in  motors  designed  for  use  with  alternating  currents 
are  particularly  complex.    The  interaction  of  the  flux  of  the  field 
coils  and  that  of  the  armature  coils,  one  or  both  of  which  may  be 
shifting,  the  inductance,  hysteresis  and  eddy  currents  necessarily 
developed  in  a  machine  in  which  alternating  currents  flow  through 
coils  embracing  soft  iron  cores,  render  the  mathematical  treatment 
of  the  problem  more  intricate  than  is  desirable  in  an  elementary 
text  book.    In  the  following  pages  therefore,  we  can  do  no  more 
than  glance  at  the  fundamental  principles  of  a  few  of  the  simpler 
forms. 

658.  Classes  of  Alternating  Current  Motors. — Alternating  cur- 
rent motors  are  usually  classed  under  the  following  heads: 

(a)  Series  motors. 

(b)  Synchronous  motors. 

(c)  Repulsion  motors. 

(d)  Induction  motors. 

The  distinction  between  these  will  be  brought  out  as  we  proceed. 

659.  Series  Motors. — In  Par.  604  it  was  shown  that  changing 
the  direction  of  the  current  supplied  to  a  shunt  motor  did  not 
alter  the  direction  of  rotation.    The  same  could  have  been  shown 
for  the  series  motor.    At  first  sight,  therefore,  it  would  seem  that 
whether  supplied  with  direct  or  with  alternating  current,  these 
motors  would  operate  equally  well.     In  the  case  of  the  shunt 
motor  however,  the  inductance  of  the  field  coils  is  much  greater 
than  that  of  the  armature  coils.    The  current  through  the  field 
coils  therefore  lags  much  more  than  that  through  the  armature 
(Par.  617).    The  torque  is  a  maximum  when  the  armature  current 
and  the  field  flux  reach  their  maxima  simultaneously,  but  since 
the  field  and  the  armature  currents  differ  in  phase,  but  little  power 
is  developed.    The  shunt  motor,  therefore,  is  not  used  with  alter- 
nating currents. 


534 


ELEMENTS  OF  ELECTRICITY. 


In  the  series  motor,  the  field  and  armature  coils  being  in  series, 
there  can  be  no  phase  difference  and  the  above  objections  do  not 
apply.  When  used  with  single  phase  alternating  currents,  series 
motors  develop  great  starting  torque  and  possess  the  advantages 
and  disadvantages  described  in  Pars.  602  and  603.  They  are 
therefore  largely  used  as  railway  motors.  The  A.  C.  motors 
differ  from  the  D.  C.  motors  in  certain  minor  arrangements  by 
which  the  tendency  of  the  A.  C.  machine  to  excessive  sparking  is 
reduced.  Also,  as  in  all  other  A.  C.  machines,  the  field  cores  must 
be  laminated. 

660.  Synchronous  Motors. — Suppose  Fig.  352  to  represent  a 
rectified  portion  of  the  alternator  shown  in  Fig.  337.  AB  repre- 
sents the  field  which  is  excited  by  direct  current  and  whose  polarity 


Fig.  352. 

therefore  does  not  vary.  CD  represents  a  portion  of  the  revolving 
armature,  the  coils  supplied  with  alternating  current  from  a 
distant  source.  At  the  instant -shown  in  the  diagram,  it  will  be 
seen  that  each  pole  of  the  armature  experiences  a  force  which 
tends  to  move  CD  from  left  to  right.  If  CD  does  not  move,  it 
will  at  the  next  reversal  of  the  current  be  urged  in  the  opposite 
direction,  or  from  right  to  left.  Suppose  it  begins  to  move  from 
left  to  right.  If  before  the  moving  coil  E  arrives  beneath  F,  the 
current  through  E  reverses,  the  polarity  of  E  also  reverses  and 
E  will  be  driven  back  from  F,  in  other  words,  the  movement  of 
CD  will  be  checked.  If  E  passes  under  F  without  reversing,  it 
will  be  pulled  back  as  soon  as  it  begins  to  emerge  on  the  other 
side.  If  it  reverses  as  it  passes  under  F,  it  will  be  pushed  ahead. 
The  frequency  of  the  alternating  current  supplied  to  the  arma- 
ture being  constant,  the  relative  positions  of  the  fixed  field  poles 
and  the  rotating  armature  coils  at  the  instant  when  the  current 


ELECTRO-MECHANICS. 


535 


in  these  latter  reverses  depends  upon  the  angular  speed  of  the 
armature.  The  effect  of  variation  in  this  speed  can  be  shown 
graphically  as  follows.  In  Fig.  353  AB  represents  the  fixed  field, 
and  a,  b  and  c  represent  the  successive  positions  of  an  armature 
coil  moving  at  three  different  speeds.  If  the  armature  be  rotated 


Fig.  353. 

slowly,  the  angular  distance  between  reversals  is  small;  if  it  rotates 
rapidly,  this  angular  distance  is  large.  In  a,  the  armature  is 
turning  slowly  and  the  polarity  of  the  coil  reverses  when  the  coil 
has  travelled  through  less  angular  distance  than  that  separating 
the  field  poles.  In  6,  it  is  turning  rapidly  and  the  reversals  occur 
at  angular  distances  apart  greater  than  that  between  the  field 
poles.  In  c,  the  reversals  occur  at  the  same  angular  distance 
apart  as  that  separating  the  poles.  In  this  last  case,  the  armature 
coil  passes  over  the  distance  between  two  successive  north  poles 
of  the  field  in  the  same  time  that  a  coil  of  the  distant  alternator 
supplying  current  to  the  armature  passes  over  the  distance  be- 
tween two  successive  north  poles  of  its  field,  in  other  words,  the 
armatures  of  the  motor  and  of  the  alternator  rotate  in  electrical 
synchronism. 

For  the  sake  of  clearness  only  forces  of  attraction  are  represented 
in  these  diagrams.    It  is  seen  at  a  glance  that  only  in  the  case  of 


536  ELEMENTS  OF  ELECTRICITY. 

the  synchronous  rotation  is  the  torque  the  same  in  direction  for 
the  successive  positions  of  the  rotating  coil.  If,  therefore,  an 
alternator  be  brought  up  to  synchronous  speed  and  then  supplied 
with  alternating  current,  it  will  continue  to  rotate.  Such  machines 
are  called  synchronous  motors.  They  differ  in  a  few  minor  details 
from  alternators.  Either  the  field  or  the  armature  may  revolve 
and  they  may  be  driven  by  either  single  phase  or  polyphase 
currents. 

661.  Operation  of  Synchronous  Motors. — A  serious  objection 
to  the  single  phase  synchronous  motor  is  that  it  can  not  of  itself 
start  from  rest.    An  auxiliary  motor  is  required  to  bring  it  up  to 
synchronous  speed  before  the  current  is  turned  on.    The  polyphase 
machines  will  start  up  of  themselves,  but  even  with  these  it  is 
usual  to  employ  an  auxiliary  starter. 

Since  these  motors  must  maintain  synchronous  speed,  it  follows 
that  their  speed  does  not  vary  with  variations  in  the  load.  The 
question  then  arises  how  is  the  supply  of  power  varied  to  meet 
the  different  demands  made  upon  it.  The  force  on  an  inductor 
of  the  armature  being  I.  H.  I  (Par.  591)  varies  directly  as  the 
current.  .The  current  varies  as  the  difference  between  the  im- 
pressed E.  M.  F.  and  the  back  E.  M.  F.  (Par.  593).  The  impressed 
E.  M.  F.  is  delivered  by  the  alternator  and  is  constant.  The  back 
E.  M.  F.  varies  with  the  speed  of  rotation  of  the  armature,  hence 
also  is  constant.  If  these  two  E.  M.  F.s  reached  their  maxima 
and  minima  simultaneously,  in  other  words,  if  they  were  in  phase, 
the  difference  between  them,  and  hence  the  current,  would  be  a 
minimum.  If,  however,  the  armature  coils  should  fall  back  a  few 
degrees  in  angular  position,  still  preserving  synchronous  rotation, 
the  two  E.  M.  F.s  would  no  longer  be  in  phase,  their  difference 
would  increase  and  a  greater  current  would  flow.  When,  therefore, 
a  load  is  thrown  on  a  synchronous  motor,  the  armature  drops 
back  a  few  degrees  and  thus  exerts  a  greater  torque.  If  the  load 
be  excessive,  the  machine  is  thrown  out  of  synchronism  and  stops. 

662.  The    Repulsion    Motor. — The    repulsion    motor,    shown 
diagrammatically  in  Fig.  354,  consists  of  an  ordinary  D.   C. 
armature  placed  in  a  field  produced  by  a  single  phase  alternating 
current.    As  the  field  alternates,  an  E.  M.  F.  is  induced  in  every 
coil  in  the  armature  except  in  the  two  at  the  opposite  ends  of  the 
horizontal  diameter.    The  direction  of  these  E.  M.  F.s  for  an  in- 


ELECTRO-MECHANICS. 


537 


creasing  flux  from  N  is  indicated  by  the  arrowheads  in  the  dia- 
gram. No  current  is  produced  since  the  E.  M.  F.s  in  the  two 
halves  of  the  armature  are  equal  and  opposed.  If  a  brush  be  ap- 
plied to  the  commutator  so  as  to  touch  two  adjacent  segments,  a 
current  will  be  produced  in  the  coil  thus  short-circuited.  If  the 


brushes  be  applied  to  the  terminals  of  the  coils  A  and  B,  the 
resulting  flux  in  these  coils  will  be  opposite  and  parallel  to  the 
field  and  hence  no  torque  will  be  developed.  If,  however,  the  coils 
D  and  E  be  short-circuited,  the  flux  in  these  coils,  as  shown  in 
the  diagram,  will  be  oblique  to  the  field,  D  will  be  repelled  from 
N  and  E  will  be  repelled  from  S  and  clockwise  rotation  will  ensue. 
When  the  field  is  reversed,  the  flux  in  the  coils  is  also  reversed 
and  the  rotation  will  continue  in  the  same  direction.  As  thus 
described,  only  the  coils  in  the  positions  D  and  E  contribute  to 
the  torque.  If  the  brushes  be  enlarged  so  as  to  short-circuit  a 
number  of  adjacent  coils,  all  of  these  coils  will  contribute  to  the 
turning  moment.  Finally,  if  the  brushes  be  connected  as  shown, 
currents  will  flow  through  the  remaining  coils  and  the  torque  will 
be  correspondingly  increased. 

It  will  be  noted  that  there  is  no  direct  electrical  connection  with 
the  armature  of  this  machine  and  that  the  currents  are  produced 
by  induction.  It  is  therefore  a  true  induction  motor. 

663.  Principle  of  Induction  Motor. — The  principle  of  the 
induction  motor  will  be  understood  from  the  following. 

SNS,  Fig.  355,  represents  a  series  of  magnetic  poles,  alternating 
in  polarity  and  moving  steadily  from  right  to  left  as  indicated  by 
the  arrow.  Beneath  these  there  is  what  may  be  compared  to  a 


538 


ELEMENTS  OF  ELECTRICITY. 


copper  ladder  with  heavy  copper  rungs.  Consider  the  opening 
A  BCD  in  this  ladder.  At  the  instant  shown  it  is  penetrated  by 
the  lines  of  force  from  N,  but  as  AT  is  moving  off  to  the  left,  the 
number  of  lines  embraced  is  decreasing  and  there  is  therefore 
induced  a  clockwise  current  in  the  direction  ABCD  (Par.  421). 
In  the  adjacent  opening  ABEF,  the  number  of  lines  embraced 
is  increasing  and  there  is  therefore  induced  a  counter-clockwise 
current  in  the  direction  ABEF,  that  is,  the  E.  M.  F.  in  the  copper 
surrounding  both  of  these  openings  produces  a  current  from  A  to 


O 


O       O 


Fig.  355. 

B.  Since  AB  is  a  conductor  carrying  a  current  and  placed  in  a 
magnetic  field,  it  experiences  a  force  urging  it  to  follow  along  after 
the  moving  pole  (Par.  352).  In  a  similar  manner  it  can  be  shown 
that  the  rungs  under  the  south  poles  are  also  urged  to  the  left. 
Reflection  will  show  that  this  movement  is  also  a  consequence  of 
Lenz's  law  (Par.  430). 

Although  the  induced  E.  M.  F.  be  small,  the  currents  in  the 
copper  rungs  are,  on  account  of  the  low  resistance,  very  large  and 
the  force  I.  H.  I  on  the  rungs  (Par.  356)  is  also  large. 

Suppose  now  the  copper  ladder  to  be  bent  into  a  cylindrical 
shape  and  fixed  upon  an  axis  like  a  squirrel  cage  (Fig.  356),  and 
suppose  the  moving  poles  to  be  formed  into  a  ring  surrounding  this 
cylinder,  and  their  movement  of  translation  to  be  converted  into  a 
movement  of  rotation.  Corresponding  rotation  will  be  produced 
in  the  squirrel  cage,  which  by  a  suitable  pulley  or  by  gearing  could 
be  made  to  do  mechanical  work.  We  have  thus  produced  rotation 


ELECTRO-MECHANICS. 


539 


in  the  cage  by  rotating  the  magnetic  field  about  it,  but  the  thought 
arises  at  once  that  the  energy  expended  in  rotating  the  field 
might  better  have  been  applied  to  the  cage  direct.  However,  it 
will  now  be  shown  that  it  is  possible  to  produce  a  rotating  field 
without  resorting  to  mechanical  rotation. 


Fig.  356. 

664.  Production  of  Rotating  Field. — Suppose  Fig.  357  to  repre- 
sent a  ring  wound  stationary  iron  frame  and  suppose  there  are 
connected  to  the  winding  at  points  90°  apart  the  leads  CC'  and 
DD'  from  a  two  phase  alternator  similar  to  the  one  shown  in 
Fig.  341.  Suppose  we  start  with  the  armature  in  the  position 


c' 


shown  in  that  figure.  At  this  instant  the  current  in  the  leads  CC' 
is  a  maximum  and  that  in  DD'  is  zero.  Application  of  the  right 
hand  rule  shows  that  the  current  entering  at  C  and  leaving  at  C' 
produces  a  south  pole  at  C  and  a  north  pole  at  C'.  The  current 


540  ELEMENTS  OF  ELECTRICITY. 

entering  at  C  now  begins  to  decrease,  while  an  increasing  current 
starts  in  at  D.  Currents  leave  by  C'  and  Df  and  a  north  pole  is 
produced  between  C'  and  Df. 

When  the  current  at  C  has  dwindled  to  zero,  the  entire  current 
enters  at  D  and  leaves  by  Df.  A  north  pole  is  therefore  produced 
at  D'. 

Without  carrying  this  explanation  farther,  it  is  seen  that  during 
one  complete  cycle  a  north  pole  starts  at  C'  and  travels  in  a 
clockwise  direction  entirely  around  the  iron  frame,  a  corresponding 
south  pole  keeping  pace  at  the  opposite  end  of  the  diameter  of  the 
ring.  The  effect  is  therefore  the  same  as  if  the  frame  work  had 
held  a  pair  of  permanent  magnetic  poles  and  had  been  rotated 
through  [360°.  In  the  actual  case,  however,  there  has  been  no 
mechanical  motion  and  no  waste  of  energy  in  overcoming  friction, 
such  as  would  have  occurred  had  the  heavy  iron  frame  been 
rotated.  A  squirrel  cage  placed  inside  of  this  ring  would  have 
been  rotated  by  the  rotating  poles. 

The  rotating  field  described  above  was  produced  by  a  two-phase 
current.  It  may  also  be  produced  by  a  tri-phase  current. 

665.  The  Induction  Motor. — The  induction  motor  is  based 
upon  the  foregoing  principles.  The  rotating  cage,  although  it 
resembles  the  armature  of  other  motors,  is  not  strictly  an  armature 
since  it  has  no  electrical  connection  with  the  power  circuit.  It  is 
therefore  called  the  rotor,  the  surrounding  magnetic  field  being 
called  the  stator.  This  is  the  usual  arrangement  but  it  is  quite 
possible  to  have  the  field  the  rotating  member. 

The  inductors  are  of  copper  as  described  above,  and  in  order  to 
insure  penetration  by  the  lines  of  force  of  the  field,  the  interior 
of  the  rotor  is  built  up  of  laminated  iron  (Par.  565),  in  fact,  the 
copper  inductors  are  generally  embedded  in  slots  in  this  laminated 
core.  The  stator  is  likewise  laminated  and,  instead  of  being  ring 
wound  as  described  in  the  preceding  paragraph,  it  is  wrapped 
somewhat  as  shown  in  Figs.  337  and  339. 

If  the  rotor  revolved  synchronously  with  the  rotating  field, 
there  would  be  no  cutting  of  lines  of  force  by  the  inductors,  hence 
no  induced  current  and  no  torque  developed.  In  order  then  to 
develop  torque  the  rotor  must  run  below  synchronism.  It  would 
therefore  seem  that  the  slower  the  rotor  turned  the  greater  would 
be  the  torque,  but  this  is  not  correct.  Examination  of  Fig.  355 
will  show  that  as  the  pole  N  moves  over  the  interval  ABEF,  an 


ELECTRO-MECHANICS.  541 

upward  flux  is  produced,  that  is,  a  flux  tending  to  demagnetize  N. 
The  force  on  an  inductor  is  I.  H.  I  (Par.  356),  but  when  the  speed 
falls  below  a  certain  point,  the  field  H  is  demagnetized  more 
rapidly  than  /  increases  and  the  total  force  therefore  falls  off.  If, 
therefore,  an  increasing  load  be  applied  to  one  of  these  motors,  it 
will  slow  down  until  the  maximum  torque  is  developed,  after 
which,  if  the  load  be  further  increased,  it  will  come  to  a  stop. 

If  one  of  these  motors  is  to  start  from  rest  under  load,  as  for 
example  in  operating  an  elevator,  it  is  desirable  that  the  maximum 
torque  should  be  exerted  at  starting.  This  may  be  attained  by 
constructing  the  rotor  so  that  the  resistance  of  the  inductors  may 
be  varied.  The  resistance  is  introduced  at  starting  and  the  cur- 
rents through  the  inductors  are  thus  kept  down  so  that  the  de- 
magnetizing effect  described  above  will  not  be  too  great.  As  the 
motor  gathers  headway,  this  resistance  may  be  cut  out. 


HIGH  POTENTIAL.  543 


PART  VI. 
HIGH  POTENTIAL. 


CHAPTER  46. 

DISCHARGE   OF   ELECTRICITY   THROUGH   GASES. 

666.  High  Potential.— The  two  following  chapters,  with  which 
we  conclude  this  book,  treat  of  the  discharge  of  electricity  through 
gases  and  of  electrical  oscillations.    While  these  subjects  stand 
somewhat  apart  from  the  divisions  which  we  have  hitherto  con- 
sidered, they  can  not  be  said  to  be  very  intimately  interrelated, 
and  they  are  here  classed  under  one  heading  mainly  because 
their  most  characteristic  phenomena  are  usually  produced  by 
the  use  of  high  voltages.    The  title  "high  potential"  must  not 
therefore  be  regarded  as  descriptive  but  rather  as  used  to  avoid 
the  comprehensive  but  still  more  indefinite  designation  "mis- 
cellaneous." 

667.  Conductivity  of  Gases. — Gases  are  ordinarily  the  most 
perfect  of  non-conductors.    In  the  list  of  these  bodies  given  in 
Par.  20,  air  was  placed  at  the  foot.    However,  under  certain  con- 
ditions described  below   (Par.  680)  their  conductivity  can  be 
greatly  increased.    Although  some  of  these  conditions  have  been 
known  for  upwards  of  fifty  years,  it  is  only  within  comparatively 
recent  times  that  this  subject  has  been  systematically  investi- 
gated, and  as  a  result  of  these  studies  much  light  has  been  thrown 
both  upon  the  mechanism  of  conduction  and  upon  the  ultimate 
nature  of  electricity  itself. 

668.  Discharge  Through  Moderate  Vacua. — Fig.  358  represents 
the  arrangement  already  described  in  Par.  525.     AB  is  a  long 
glass  tube  into  each  end  of  which  is  sealed  a  platinum  wire  ter- 
minating on  the  inside  in  a  small  disc.    The  platinum  wires  are 
connected  to  the  opposite  sides  of  the  spark  gap  GH  of  an  indue- 


544 


ELEMENTS  OF  ELECTRICITY. 


tion  coil.  An  air  pump  is  attached  to  a  small  tube  blown  in  one 
side  of  the  larger  tube  and  the  air  is  gradually  exhausted.  At 
first,  the  sparks  produced  by  the  coil  leap  across  the  gap  GH, 
but  as  the  air  is  exhausted  from  the  tube  these  sparks  cease  and 
a  flickering  light,  like  summer  lightning,  appears  on  the  inside. 


CATHOBE: 


ANODE 


Fig.  358. 

If  the  exhaustion  be  carried  a  little  farther,  or  to  a  pressure 
corresponding  to  about  an  inch  of  mercury,  a  luminous  column, 
the  positive  column,  extends  the  entire  length  of  the  tube  between 
the  anode  and  the  cathode.  The  spark  gap  may  now  be  very 
materially  decreased  without  a  spark  passing,  thus  showing  that 
the  conducting  power  of  the  gas  within  the  tube  has  been  greatly 
increased. 

669.  Effect  of  Magnetic  Field  on  Positive  Column.— If  while 
the  discharge  is  taking  the  form  of  the  positive  column  the  tube 
be  placed  in  a  crosswise  magnetic  field,  the  column  is  deflected 
for  apportion  of  its  length.    Thus,  if  a  horseshoe  magnet  be  placed 
as  shown  in  Fig.  358  so  that  the  tube  is  penetrated  at  right  angles 
by  a  magnetic  field  from  rear  to  front,  the  portion  of  the  column 
between  the  poles  of  the  magnet  will  be  bent  upward  as  indicated 
by  the  dotted  lines.    Application  of  the  left  hand  rule  (Par.  352) 
will  show  that  in  this  respect  the  column  behaves  as  if  it  were  a 
flexible  conductor  carrying  a  current. 

670.  Discharge  Through  High  Vacua. — If  the  exhaustion  of 
the  tube  described  in  Par.  668  be  continued,  when  the  pressure 
has  been  reduced  to  about  that  of  two  millimeters  of  mercury, 
the  following  changes  are  observed.    The  surface  of  the  cathode 
is  covered  with  a  thin  luminous  layer.    Adjoining  this  there  is  a 


HIGH  POTENTIAL. 


545 


dark  space  C  (Fig.  359),  the  Crookes  dark  space,  which  enlarges 
as  the  pressure  diminishes,  and  adjoining  this  space  there  is  a 
luminous  region  D,  the  negative  glow.  Beyond  this  there  is  a 
second  dark  space  F,  the  Faraday  dark  space,  followed  by  the 
positive  column  E  which  is  now  broken  up  into  striae,  transverse 


Fig.  359. 

luminous  discs.  A  potential  sufficient  to  produce  in  air  a  spark 
one-eighth  ^of  an  inch  in  length  will  now  cause  a  discharge  through 
a  tube  twenty  inches  long.  Tubes  exhausted  to  this  extent  are 
called  Geissler  tubes. 

If  the  exhaustion  be  carried  to  about  one-millionth  of  an 
atmosphere,  the  tube  is  called  a  Crookes  tube.  The  luminous 
spaces  entirely  disappear,  the  Crookes  dark  space  spreading 
throughout  the  tube,  but  the  glass  itself  now  begins  to  phosphor- 
esce with  a  color  which  varies  with  its  composition.  Soda  glass 
glows  with  a  fine  green  color;  lead  glass  with  a  pale  blue.  The 
resistance  is  now  much  greater  and  increases  rapidly  so  that  if 
the  exhaustion  be  carried  slightly  farther  it  becomes  no  longer 
possible  to  send  a  discharge  through  the  tube. 

671.  Cathode  Rays. — It  was  discovered  by  Crookes  that  the 
phosphorescence  of  the  glass  tube  described  in  the  preceding 
paragraph  is  produced  by  certain  invisible  radiations  proceeding 


a 


Fig.  360. 

from  the  cathode,  and  these  have  accordingly  been  named  cathode 
rays.  It  may  be  shown  that  they  leave  the  cathode  at  right 
angles  to  the  latter's  surface.  In  the  V-shaped  Crookes  tube 
shown  in  a,  Fig.  360,  whether  A  or  B  be  used  as  the  anode,  only 
B,  the  arm  up  which  the  cathode  points,  will  phosphoresce. 


546  ELEMENTS  OF  ELECTRICITY. 

If  the  cathode  be  given  a  concave  shape,  a  piece  of  platinum 
foil  placed  at  the  focus  may  be  raised  to  a  red  heat  by  the  rays. 
Many  substances,  even  when  not  highly  heated,  fluoresce  or 
emit  brilliant  light  when  placed  in  the  path  of  these  rays. 

672.  Nature   of  Cathode   Rays. — Investigations   lead   to   the 
belief  that  the  cathode  rays  consist  of  minute  material  particles 
carrying  electrical  charges  and  moving  with  a  velocity  so  great 
that  they  cause  the  bodies  upon  which  they  strike  to  emit  light 
or  fluoresce.     These  particles  have  been  'variously  named  cor- 
puscles, electrons  and  negative  ions. 

In  the  Crookes  tube  shown  in  6,  Fig.  360,  a  mica  cross  B  is 
mounted  upon  the  anode  A  and  when  the  tube  is  in  operation  a 
distinct  shadow  of  this  cross  appears  upon  the  phosphorescent 
background  at  D.  B  therefore  screens  the  glass  from  the  rays 
from  C.  Since  B  is  transparent,  the  cathode  rays  are  not  of  the 
nature  of  ordinary  light. 

If,  instead  of  the  cross,  a  very  delicate  little  paddle  wheel  be 
mounted  at  B  and  so  placed  that  the  rays  from  C  strike  upon 
the  vanes  of  one  side  only,  it  will  take  up  a  motion  of  rotation 
as  if  it  had  been  bombarded  with  small  particles  from  C. 

673.  Effect  of  Magnetic  Field  on  Cathode  Rays.— The  cathode 
rays  are  deflected  by  a  magnetic  field.     In  the  Crookes  tube 


Fig.  361. 

shown  in  Fig.  361,  a  diaphragm  B  with  a  narrow  slit  is  placed  in 
front  of  the  cathode.  Beyond  this  diaphragm  and  lying  along 
the  axis  of  the  tube  is  a  vertical  sheet  of  mica  coated  with  chalk. 
The  narrow  beam  of  rays  through  the  slit  causes  in  this  chalk 
a  bright  line  of  fluorescence  CD.  If  now  a  horseshoe  magnet  be 
placed  as  shown  in  Fig.  358,  the  field  running  from  rear  to  front, 
the  beam  of  rays  will  be  deflected  in  the  same  direction  as  the 
positive  column  (Par.  669).  There  is,  however,  a  great  difference 
in  the  two  cases.  The  positive  column  is  simply  deflected  as  it 
passes  through  the  field  and  beyond  this  field  returns  to  its  original 
direction;  the  cathode  rays,  after  passing  beyond  the  field,  continue 


HIGH  POTENTIAL.  547 

in  their  deflected  direction  and  terminate  upon  the  side  of  the  tube 
«t£ 

674.  Effect  of  Electric  Field  Upon  Cathode  Rays.— Cathode 
rays  are  also  deflected  by  an  electric  field.    Thus,  if  the  tube  shown 
in  Fig.  361  be  placed  between  two  parallel  metal  plates,  one  above 
and  the  other  below,  and  if  the  upper  plate  be  charged  positively, 
the  rays  will  be  deflected  upward  in  the  direction  CE.    The  con- 
clusion is  that  the  corpuscles,  or  little  particles  of  which  the  cathode 
rays  are  composed,  carry  negative  charges  and  are  consequently 
attracted  by  the  positively  charged  and  repelled  by  the  negatively- 
charged  plate. 

The  same  conclusion  might  have  been  drawn  from  the  deflec- 
tion produced  in  the  cathode  rays  by  a  magnetic  field.  Since 
these  rays,  although  moving  in  opposite  direction,  were  deflected 
in  the  same  direction  as  the  positive  column,  they  must  have 
constituted  a  current  of  negative  electricity. 

675.  Nature  of  Charge  Carried  by  Corpuscle. — The  correctness 
of  the  above  conclusion  that  the  corpuscles  carry  negative  charges 


Fig.  362. 

is  experimentally  confirmed  as  follows.  In  the  two-chambered 
Crookes  tube  shown  in  Fig.  362,  B  is  a  metal  diaphragm  pierced 
with  a  narrow  slit  and  together  with  A  constituting  the  anode. 
C  is  the  cathode.  The  side  tube  D  contains  a  metal  cylinder  with 
a  narrow  opening  at  F  and  with  a  connection  at  G  by  which  it  may 
be  grounded.  Within  this  cylinder  but  insulated  from  it  there 
is  a  second  cylinder  with  a  terminal  at  H.  An  electrometer  is 
connected  to  this  terminal.  Normally,  the  cathode  rays  pass 
through  the  slit  in  the  diaphragm  and  strike  at  E  where  they 
produce  a  luminous  spot.  By  means  of  a  magnet  these  rays  are 


548  ELEMENTS  OF  ELECTRICITY. 

deflected.  The  instant  that  they  are  bent  enough  to  enter  the 
opening  at  F,  the  electrometer  indicates  that  the  inner  cylinder 
has  received  a  negative  charge. 

676.  Positive  Rays. — If  the  cathode  of  a  Crookes  tube  be 
pierced  with  small  holes,  luminous  rays  passing  through  these 
holes  will  be  seen  at  the  back  of  the  cathode.    These  are  found 
to  consist  of  positively-charged  ions  and  are  accordingly  called 
positive  rays,  sometimes  also  canal  rays. 

677.  Lenard  Rays. — While  the  cathode  rays  do  not  penetrate 
the  Crookes  tube  in  which  they  are  produced,  Lenard  found  that 
if  a  small  window  of  aluminum  foil  be  let  into  the  side  of  the  tube, 
the  effect  of  the  rays  could  be  detected  for  a  distance  of  several 
inches  in  the  air  on  the  outside.    Since  the  fact  that  these  rays 
apparently  pass  through  metal  appears  contrary  to  the  theory 
that  they  consist  of  small  material  particles,  these  exterior  rays 
were  at  first  considered  to  be  something  different  and  were  called 
Lenard  rays.    It  is  now  known  that  they  are  identical  with  cathode 
rays.    It  is  thought  that  the  cathode  rays  on  the  interior  of  the 
tube  do  not  actually  penetrate  the  aluminum  but  strike  it  with 
such  energy  that  the  percussion  drives  off  ions  from  the  outer 
surface. 

678.  X-Rays. — In  addition  to  heating  the  objects  upon  which 
they  fall,  the  cathode  rays  cause  these  objects  to  emit  rays  of  a 
very  remarkable  penetrative  power.     Rontgen  accidently  dis- 
covered this  fact  in  1895.    He  noticed  that  a  covered  photographic 
plate  in  his  laboratory  became  fogged  by  the  rays  from  a  Crookes 
tube  with  which  he  was  working.    It  was  known  that  the  effect 
of  the  Lenard  rays  extended  only  a  few  inches  beyond  the  tube 
and  he  realized  that  he  was  dealing  with  an  unknown  form.    He 
therefore  designated  them  as  X-rays,  though  later,  in  his  honor, 
they  were  called  Rontgen  rays. 

They  travel  with  the  velocity  of  light,  penetrate  all  bodies  to 
some  extent,  are  not  reflected  or  refracted  and  are  unaffected  by 
electric  or  magnetic  fields.  Their  penetration  into  the  metals 
varies  inversely  as  the  atomic  weights  of  these  metals.  Lead, 
whose  atomic  weight  is  207,  is  therefore  the  metal  most  frequently 
used  as  a  screen  for  these  rays. 

They  excite  powerful  phosphorescence  in  many  substances. 
Advantage  is  taken  of  this  in  the  fluoroscope.  This  consists  of  a 


HIGH  POTENTIAL. 


549 


light-proof  frame  shaped  like  the  frustum  of  a  pyramid.  Over 
the  larger  end  is  spread  a  cardboard  coated  with  barium  platino- 
cyanide.  The  smaller  end  of  the  frustum  is  arranged  so  as  to  be 
applied  to  an  observer's  face  as  shown  in  Fig.  363.  When  exposed 
to  the  X-rays,  the  barium  salt  glows  with  a  yellowish  color  and 
to  the  observer  the  effect  is  as  if  he  were  looking  through  a  frosted 
glass  window  of  that  color.  If  the  hand  be  interposed  between 
the  source  of  the  X-rays  and  the  fluoroscope  and  be  applied  to 
the  coated  cardboard,  the  X-rays  penetrate  the  flesh  more  easily 
than  they  do  the  bones  and  the  outline  or  shadow  of  the  bones 
is  clearly  seen.  This  instrument  is  used  in  surgery  in  the  examina- 
tion of  fractures,  location  of  foreign  bodies,  etc. 


Fig.  363. 


X-ray  photographs  or  sciagraphs  (shadow  pictures)  are  made 
in  a  similar  manner.  The  sensitive  plate  enclosed  in  its  holder  is 
usually  placed  on  a  table,  the  patient  placing  immediately  above 
the  plate  the  part  of  his  body  to  be  photographed.  Exposure  to 
the  rays  is  then  made  and  the  plate  is  developed.  In  this  way  the 
greatest  steadiness  is  secured. 

In  making  these  sciagraphs  a  special  form  of  Crookes  tube, 
a  so-called  focusing  tube,  is  used.  As  shown  in  Fig.  363,  the  cathode 
is  concave  and  the  anode  located  at  its  focus  is  a  flat  plate  of 
platinum  inclined  at  an  angle  of  45°  to  the  cathode  rays.  The 
X-rays  thus  emanate  from  a  small  area  and  more  clear-cut 
shadows  are  produced. 

These  rays  are  particularly  destructive  to  cells.  They  are 
therefore  used  in  medicine  for  the  treatment  of  superficial  forms 
of  cancer,  tuberculosis  and  skin  diseases,  but  they  are  not  selec- 
tive and  destroy  the  healthy  as  well  as  the  diseased,  producing 
burns  which  are  very  difficult  to  heal. 


550  ELEMENTS  OF  ELECTRICITY. 

679.  Becquerel  Rays. — In  1896  Becquerel  in  investigating  the 
properties  of  phosphorescent  bodies  discovered  that  the  compounds 
of  the  metal  uranium  emitted  rays  which  partook  of  the  nature 
of  both  the  cathode  rays  and  the  X-rays.    It  was  soon  found  that 
these  Becquerel  rays  were  not  confined  to  uranium  compounds 
but  were  produced  by  other  substances.     Those  bodies  which 
emit  these  rays  are  said  to  be  radio-active. 

•  The  principal  ore  of  uranium  is  the  oxide,  pitch  blende.  The 
Curies  found  that  the  residue  left  after  extracting  the  uranium 
from  this  ore  was  more  radio-active  than  the  uranium  itself,  and 
irTl898  they  succeeded  in  separating  from  this  residue  a  compound 
of  a  new  element,  radium,  whose  radio-activity  was  over  a  mil- 
lion times  greater  than  that  of  uranium.  Radium  has  not  yet 
been  isolated  but  is  known  to  be  a  metal  chemically  allied  to 
barium.  It  exists  in  such  minute  quantities  that  from  a  ton  of 
the  ore  only  about  two-tenths  of  a  gram  of  the  impure  chloride 
or  bromide  is  obtained.  Associated  with  it  are  polonium  and 
actinium,  two  still  rarer  metals  possessing  similar  properties. 

The  Becquerel  rays  are  complex  but  by  passing  them  through 
a  magnetic  field  they  may  be  resolved  into  three  types  called 
the  alpha,  the  beta  and  the  gamma  rays,  respectively.  The  alpha 
and  the  beta  rays  are  deflected,  but  in  opposite  directions;  the 
alpha  rays  being  positive  rays,  the  beta  rays  being  negative  or 
cathode  rays.  The  gamma  rays  are  unaffected  by  the  magnetic 
field  and  are  allied  to,  if  not  identical  with,  the  X-rays.  They 
have  almost  incredible  penetrative  power,  being  able  to  penetrate 
upwards  of  a  foot  of  solid  iron. 

680.  Increase  of  Conductivity  of  Gases. — While,  as  already 
stated,  the  conductivity  of  a  gas  is  normally  very  small,  there 
are  many  widely  different  ways  in  which  it  may  be  greatly  in- 
creased.   Thus,  a  gas  becomes  a  conductor  if  it  be  highly  heated, 
or  if  it  be  mixed  with  gas  drawn  from  the  vicinity  of  glowing 
metals  or  of  the  electric  arc,  or  if  an  electric  spark  be  passed 
through  it,  or  if  it  be  exposed  to  any  of  the  cathode,  Lenard, 
Becquerel  or  X-rays  described  above,  or  if  it  be  exposed  to  ultra- 
violet light,  etc.,  etc.    This  increase  in  conductivity  is  best  shown 
by  means  of  a  gold  leaf  electroscope.    So  long  as  the  surrounding 
air  remains  in  its  normal  state,  the  leaves,  if  charged,  remain 
diverging,  or  if  they  fall  together,  do  so  very  slowly.     If,  how- 
ever, the  air  be  rendered  conductive,  as  for  example  by  holding 


HIGH  POTENTIAL. 


551 


within  a  foot  or  so  of  the  leaves  a  minute  quantity  of  a  radium 
salt,  the  leaves  collapse  at  once.  The  following  experiment 
illustrates  the  production  of  conductivity  by  the  X-rays.  In 
Fig.  364,  A  is  an  X-ray  tube  enclosed  in  a  thick  box  of  lead  with 
a  small  aperture  in  the  top  through  which  the  rays  may  emerge. 
Immediately  above  this  opening  there  is  an  inverted  funnel  F 


Fig.  364. 

which  communicates  through  a  glass  tube  with  the  jar  B  in  which 
the  electroscope  is  suspended.  The  X-rays  render  the  air 
through  which  they  pass  conductive,  for  if  suction  be  applied  to 
the  tube  C  so  as  to  draw  the  air  within  F  over  into  the  jar  B,  the 
leaves  collapse  as  soon  as  this  air  enters  the  jar. 

681.  lonization  of  Gases.— In  the  preceding  paragraph  we  saw 
how  the  air  within  the  funnel  F  (Fig.  364)  was  rendered  conduc- 
tive by  the  action  of  the  X-rays  and  how  it  retained  this  con- 
ductivity after  it  had  been  drawn  over  into  the  jar  B.  If,  however, 
there  be  placed  in  the  tube  between  F  and  B  a  plug  of  glass  wool, 
the  air  from  F  after  passing  through  this  plug  will  be  found  to 
have  lost  its  conductivity.  The  same  thing  happens  if  this  air 
be  drawn  through  a  metal  tube  of  fine  bore,  or  if  it  be  caused  to 
bubble  through  water.  Since,  therefore,  the  conductivity  of 
the  air  may  be  thus  removed  by  filtration,  it  is  but  natural  to 
ascribe  it  to  the  presence  of  material  particles.  Furthermore,  the 
conductivity  is  removed  if  the  air  be  passed  between  two  parallel 
metal  plates  between  which  a  strong  electric  field  is  maintained. 
These  material  particles  must  therefore  carry  electric  charges, 
and  since  the  air  as  a  whole  shows  no  sign  of  a  charge,  there  must 
be  an  equal  amount  of  positive  and  negative  charges  present. 
The  theory  was  therefore  advanced  by  Thomson  that  the  con- 


552 


ELEMENTS  OF  ELECTRICITY. 


ductivity  of  a  gas  is  due  to  the  presence  of  particles  or  part  mole- 
cules, called  ions,  some  positively  and  others  negatively  charged. 
These  negatively-charged  particles  are  found  to  be  identical  with 
the  corpuscles  of  the  cathode  ray.  The  production  of  these  ions, 
or  ionization,  is  brought  about  by  any  of  the  agents  mentioned 
in  the  preceding  paragraph.  The  explanation  advanced  is  that 
the  ions  or  corpuscles  associated  with  these  various  agencies  are 
moving  with  such  velocity  that  when  they  come  into  collision 
with  the  molecules  of  the  gas  through  which  they  pass,  they 
break  these  molecules  up  into  other  ions. 

682.  Investigation  of  Corpuscles. — From  the  time  that  the 
theory  was  advanced  that  the  cathode  rays  consisted  of  charged 
corpuscles  moving  with  high  velocity,  efforts  were  directed  to 
determine  the  mass  of  these  corpuscles,  the  charge  which  they 
carry  and  the  velocity  with  which  they  move.  In  the  solution 
of  this  problem  the  work  of  J.  J.  Thomson  has  been  especially 
noteworthy.  We  can  do  no  more  than  give  a  bare  outline  of  his 
methods. 

His  first  step  was  to  determine  the  relation  between  these 
three  quantities,  and  this  he  did  as  follows.  In  the  neck  of  the 
two-chambered  Crookes  tube  shown  in  Fig.  365,  B  and  D  are  two 


Fig.  365. 

thick  metal  diaphragms  pierced  by  an  opening  about  a  millimeter 
in  width.  The  diaphragm  B  forms  a  part  of  the  anode  A.  The 
rays  from  the  cathode  C  pass  in  a  narrow  line  through  the  slits 
in  B  and  D  and  produce  a  small  luminous  spot  at  E  on  the  far 
side  of  the  other  end  of  the  tube. 

Let  the  mass  of  each  corpuscle  be  ra  grams,  its  velocity  be  v 
centimeters  per  second  and  its  charge  q  electro-magnetic  absolute 
units  (Par.  536).  Each  moving  corpuscle  is  equivalent  to  a  cur- 
rent whose  strength  is  vq  absolute  units.  If  the  tube  be  placed  in 
and  at  right  angles  to  a  uniform  magnetic  field  of  intensity  H, 
each  corpuscle  will  be  acted  upon  by  a  force  vqH  at  right  angles 


HIGH  POTENTIAL.  553 

to  its  path  (Par.  356).  Now  it  is  shown  in  mechanics  that  if  a 
body  moving  with  uniform  velocity  be  acted  upon  by  a  constant 
force  at  right  angles  to  its  path,  then  the  body  will  move  upon  the 
arc  of  a  circle.  The  radius  of  this  circle  is  given  by  the  expression 

r  =  -j->S  being  the  force  at  right  angles  to  the  path.  The  deflected 
corpuscles  therefore  move  upon  an  arc  whose  radius  is 

_  mv2       mv 
~  vqH~^  qH 

If  the  positive  direction  of  the  field  be  from  front  to  rear,  the 
rays  DE  will  be  curved  downward  to  DF.     DE,  the  tangent 
to  the  arc,   and  EF  are  measured, 
whence  the  radius  of  the  circle  is  de- 
termined thus: 

The  triangles  CDE  and  DFE  (Fig. 
366)  being  similar 

EF:DE::DE:CE 
whence 

EF'.DE  ::DE:2r  +  EF 


whence  Fig  366 


The  intensity  of  the  field  being  measured,  we  have  H  and  r,  and 

the  value  of  —  becomes  known. 
Q 

683.  Velocity  of  Corpuscles.  —  The  velocity  v  of  the  moving  cor- 
puscles was  determined  by  Thomson  as  follows.  Coils  were  placed 
in  front  and  rear  of  the  tube  shown  in  Fig.  365  and  a  uniform  trans- 
verse magnetic  field  H  established.  If  the  positive  direction  of 
this  field  was  from  front  to  rear,  the  rays  were  deflected  downward 
by  a  force  vqH. 

The  parallel  metal  plates  P  and  N  were  connected  to  the  ter- 
minals of  the  battery,  thus  establishing  in  the  tube  a  vertical 
electric  field  F.  If  the  plate  P  were  positively  charged,  the  rays 
would  be  deflected  upward  with  a  force  Fq  (Par.  674).  By  vary- 
ing either  field  (generally  the  magnetic  field)  they  could  be  so 
adjusted  that  the  tendency  of  one  to  bend  the  rays  down  was 


554  ELEMENTS  OF  ELECTRICITY. 

exactly  balanced  by  the  tendency  of  the  other  to  bend  the  rays 
upward.  At  the  instant 

vq  H  —  Fq 

whence  v  =  -77 

rz 

and  knowing  F  and   H,  the 

velocity  v  becomes  known.  This  velocity,  when  the  tube  is  highly 
exhausted,  is  about  one-tenth  of  the  velocity  of  light,  and  is  in- 
dependent of  the  nature  of  the  gas  within  the  tube. 

By  inserting  this  value  of  v  in  the  expression  deduced  in  the 
preceding  paragraph  we  obtain  the  value  of  m/q,  or  the  ratio  of 
the  mass  of  the  corpuscle  to  the  charge  which  it  carries.  More 
frequently,  the  reciprocal  of  this  ratio,  or  the  ratio  of  q/m  is  given. 
According  to  the  latest  determinations  it  is  1.7x  107.  It  can  be 
shown  that  in  ordinary  electrolysis  the  ratio  of  q/m  for  the  hydrogen 
atom  is  about  104. 

684.  Mass  of  Corpuscle. — Having  thus  found  the  value  of  q/m, 
if  either  one  of  these  quantities  be  separately  obtained  the  value 
of  the  other  follows  at  once.  The  charge  q  is  the  one  usually 
determined  directly.  The  actual  process  involves  many  steps 
into  which  we  can  not  go  in  detail.  It  is  based  upon  the  following 
principles.  If  a  volume  of  saturated  vapor  be  suddenly  expanded 
its  temperature  falls  and  there  is  a  tendency  for  condensation  to 
ensue.  If  in  such  supersaturated  space  microscopic  particles  of 
dust  be  introduced,  a  fog  is  produced  at  once,  the  particles  of  dust 
facilitating  condensation  by  serving  as  nuclei  upon  which  the 
drops  form.  Now,  if  a  closed  vessel  with  an  aluminum  cover  be 
exposed  to  certain  radiations,  such  as  those  from  radium  salts, 
or  to  X-rays,  corpuscles  are  produced  in  the  gas  within  the  vessel. 
These  corpuscles  act  just  like  the  dust  in  that  they  serve  as  nuclei 
for  drops  and  in  a  supersaturated  space  cause  a  fog  to  form  at 
once.  These  drops  of  mist  are  very  minute  but  may  be  seen 
through  a  glass  and  by  suitable  observations  the  velocity  with 
which  they  slowly  settle  can  be  determined.  Knowing  this  veloc- 
ity and  the  density  of  the  gas  within  the  vessel,  by  the  applica- 
tion of  known  formulae  the  size,  and  hence  the  mass,  of  the  drops 
can  be  calculated.  The  vapor  within  the  vessel  contains  both 
positive  and  negative  ions  but  it  has  been  found  that  if  the  ex- 
pansion is  not  greater  than  one-quarter  of  the  original  volume 


HIGH  POTENTIAL.  555 

that  only  the  negative  ions  serve  as  nuclei  and  are  carried  down. 
Each  slowly-falling  drop  therefore  has  a  corpuscle  as  a  nucleus. 
The  charge  carried  by  this  corpuscle  has  been  determined  in 
several  ways.  If  the  drop  falls  between  two  horizontal  parallel 
metal  plates,  the  lower  plate  can  be  given  a  negative  charge  so 
that  its  repulsion  will  counterbalance  the  force  of  gravity  on  the 
drop,  or  may  drive  it  upward.  By  measuring  the  upward  velocity, 
the  force  exerted  upon  it  can  be  found,  and  hence  the  charge  which 
it  carries. 

Within  the  limits  of  experimental  error,  this  charge  is  found  to 
be  the  same  as  the  charge  carried  by  the  hydrogen  atom  in  ordi- 
nary electrolysis.  Since  we  saw  in  the  preceding  paragraph  that 
the  ratio  of  q  to  m  for  the  corpuscle  is  1.7  X 107,  and  for  the  hydrogen 
atom  is  104,  and  since  q  is  shown  to  be  the  same  in  the  two  cases, 
the  mass  of  the  corpuscle  is  1700  times  less  than  that  of  the  hydrogen 
atom.  On  the  other  hand,  the  mass  of  the  positive  ions  is  found 
to  agree  with  the  mass  of  the  corresponding  atoms. 

685.  Nature  of  Corpuscles. — Upon  the  nature  of  the  negative 
ions  or  corpuscles,  scientists  are  not  entirely  agreed.  From  what- 
ever substance  produced,  they  appear  to  have  the  same  mass. 
Some  therefore  maintain  that  they  are  the  true  atoms  of  a  uni- 
versal single  matter  and  that  the  fact  that  the  weights  of  the 
majority  of  the  ordinary  chemical  atoms  may  be  expressed  in 
whole  numbers  is  simply  an  expression  of  a  law  of  multiples 
which  would  follow  from  these  atoms  being  composed  of  definite 
numbers  of  corpuscles.  It  would  seem  therefore  that  we  had 
confirmed  the  belief  of  the  alchemists  that  all  matter  was  composed 
of  a  single  and  ultimate  element. 

On  the  other  hand,  a  few  deny  that  they  are  matter  and  claim 
that  they  are  portions  of  ether  in  rapid  movement. 

Whatever  be  the  nature  of  the  corpuscles  themselves,  it  is  quite 
certain  that  the  charges  which  they  carry  are  electric  atoms  in  the 
sense  that  they  are  all  the  same  and  that  no  smaller  charge  has 
yet  been  obtained.  The  atomic  character  of  these  electrons  has 
already  been  mentioned  (Par.  280). 


556 


ELEMENTS  OF  ELECTRICITY. 


CHAPTER  47. 
ELECTRIC   OSCILLATIONS. 

686.  Henry's  Theory  of  Oscillatory  Discharge  of  Leyden  Jar. — 

Seventy-five  years  ago  the  identity  of  static  and  voltaic  electricity 
was  not  regarded  as  proven.  It  had  just  been  discovered  that  a 
voltaic  current  sent  through  a  coil  wrapped  about  a  steel  bar 
converted  the  bar  into  a  magnet.  It  occurred  to  investigators 
that  this  fact  afforded  a  means  of  making  the  desired  proof.  A 

steel  needle  was  placed  in  a  coil,  one 
end  of  which  was  connected  to  the 
outer  coating  of  a  Leyden  jar  (Fig. 
367),  the  other  end  terminating  in  a 
knob  near  the  knob  which  communi- 
cated with  the  inner  lining.  When  a 
spark  was  caused  to  pass  between  the 
knobs,  this  charge  passed  through  the 
coil  and  if  it  were  of  the  same  nature 
as  voltaic  electricity  it  should  mag- 
netize the  needle.  When  this  was  done 
it  was  found,  according  to  expectation, 
that  the  needle  became  magnetized. 
Flg* 367*  However,  when  these  investigations 

were  continued  it  was  noted  that  although  the  charge  was  sent 
through  the  coil  always  in  the  same  direction,  the  polarity  of  the 
resulting  magnets  varied  in  an  anomalous  manner  so  that  it  was 
not  possible  to  predict  which  end  of  the  needle  would  be  the  north 
pole.  In  seeking  to  explain  this,  Henry  in  1842  advanced  the 
theory  that  the  discharge  of  a  Leyden  jar,  although  appearing  to 
our  senses  as  a  single  spark,  was  in  reality  an  oscillation  of  a 
current  back  and  forth,  and  the  polarity  of  the  needle  depended 
therefore  upon  the  direction  of  the  last  oscillation. 

687.  Thomson's  Mathematical  Proof  of  Oscillation.— Some  ten 
years  after  Henry  announced  his  theory,  Sir  William  Thomson 
(Lord  Kelvin)  advanced  a  mathematical  proof  of  its  correctness. 
His  deduction  may  be  shown  as  follows: 


HIGH  POTENTIAL.  557 

Suppose  that  a  Ley  den  jar  of  capacity  K  is  discharged  through 
a  conductor  of  resistance  R  and  of  inductance  L,  and  suppose 
that  at  any  given  instant  it  contains  a  charge  q.  The  energy  of 
the  electro-static  field  of  the  jar  at  this  instant  is  (Par.  97) 


This  energy  is  being  dissipated  in  two  ways;  (a)  in  establishing 
an  electro-magnetic  field  about  the  conductor  and  (b)  in  heating 
this  conductor. 

If  the  instantaneous  value  of  the  current  be  /,  the  energy  of 
the  electro-magnetic  field  is  (Par.  359)  ^  /  N,  or  since  N  =  LI 
(Par.  434) 


Since  /  =  —  -£ ,  the  rate  at  which  the  charge  is  diminishing, 
this  may  be  written 


The  rate  at  which  energy  is  being  lost  by  the  jar  is  equal  to  the 
rate  at  which  energy  is  being  gained  by  the  field  plus  the  rate  at 
which  it  is  being  expended  in  heating  the  circuit. 

The  rate  at  which  energy  is  being  lost  by  the  jar  is 

q_     dq 
K  '  dt 

The  rate  at  which  it  is  being  gained  by  the  field  is 


T 
' 


dq 


dt    dP 
The  rate  at  which  it  is  being  dissipated  in  heat  is 


whence 


whence 


q     dq  _  Tdq 

K'  dt  ~      dt 


2-i  +  ZX-0 


558  ELEMENTS  OF  ELECTRICITY. 

A  differential  equation  of  this  form  may  be  solved  by  substi- 
tuting €mt  for  q  (Murray,  Differential  Equations,  Par.  50), 
Making  this  substitution  we  have 

R  1 

whence  j  /          E 

em<(m2  +  £m+-^)=0 

which  is  satisfied  when 

m2  -f-r-fl 
or  when 


The  values  of  w  are  real  when  the  quantity  under  the  radical 
is  positive,  that  is,  when  R2  >  4  L/  K.  Designating  these  values 
of  m  by  —  mi  and  —  ra2  (since  they  are  both  negative),  the  cor- 
responding value  of  q  is 

q  =  ae-m^  +  be"™*1 

a  and  b  being  constants. 
If  t  be  made  equal  to  zero,  we  have 

q  =  a  +  b 

q  in  this  case  being  the  value  of 

the  charge  in  the  jar  just  before  the  discharge  began.  As  t  in- 
creases, corresponding  to  subsequent  time,  the  value  of  q  gets 
steadily  smaller  (since  the  exponents  of  e  are  negative),  that  is, 
the  charge  dwindles  away  without  fluctuations  or  change  of  sign. 
The  discharge  is  therefore  unidirectional. 

If,  however,  R2  is  less  than  4L/  K,  the  values  of  m  in  (I)  above 
are  imaginary.  In  this  case  we  may  proceed  as  follows: 

The  expression  for  m  is  written 


and  placing  a  =  —  y  r 
=  y  j-j*  —  -£jj  and  i  =  V—  1,  the  corresponding  roots  may 


be  written 

mi  =  a  +  pi 


=  a  — 


HIGH  POTENTIAL  559 

whence  as  above 


Q  = 

which  can  be  put  in  the  form  (Murray,  Par.  52) 
q  =  €at  (A  cos  pt  +  B  sin  00 

If  the  expression  within  the  parentheses  be  multiplied  and 
divided  by  VA2  +  B2,  we  have 

A  B  \ 

,  -cos fit  H — ,  •  sin pt} 

.VA2  +  B2  VA2  +  B2          I 

which  may  be  written 

AI  (sin  0  cos  pt  +  cos  <£  sin  00 

which  is  equal  to 

AI  sin  (pt  +  </>) 

and  substituting  above 

In  this  expression,  t  being  the  only  variable,  we  see  that  q  varies 
harmonically,  in  other  words,  the  discharge  is  oscillatory,  although, 
since  a  is  negative,  the  oscillations  gradually  die  out. 

Since  pt  is  the  variable  angle  and  t  is  time,  0  is  angular  velocity 
and  the  periodic  time  of  an  oscillation  is  27T/0.  Substituting  the 
value  of  p  from  above 

27T  47TLK 


If  R  be  very  small,  which  is  usually  the  case,  R2K2  may  be 
neglected  and  this  last  expression  reduces  to 

T  =  27T  VLK 

whence,  the  periodic  time 

increases  with  an  increase  in  L,  the  inductance,  or  in  K,  the 
capacity. 

688.  Feddersen's  Experiment  with  Revolving  Mirror.— In  1859 
Feddersen  by  a  simple  experiment  proved  the  correctness  of 
Henry's  theory  and  of  Thomson's  deductions.  The  principle  he 
employed  will  be  understood  from  the  following.  In  Fig.  368,  G 
is  the  spark  gap  of  a  Leyden  jar,  M  is  a  mirror  mounted  upon  an 
axis  about  which  it  is  capable  of  rapid  rotation,  and  P  is  a  photo- 


560 


ELEMENTS  OF  ELECTRICITY. 


graphic  plate.  If  while  the  mirror  is  rotating  a  spark  be  passed 
across  the  gap  G,  the  beam  of  light  from  this  spark  will  fall  upon 
the  mirror  and  will  be  reflected.  Owing  to  the  movement  of  M, 
this  reflected  beam  will  sweep  like  a  brush  across  P  and  when  the 
plate  is  developed  and  printed  the  path  will  be  revealed  as  a  band 
of  light.  Examination  will  show  along  the  edges  of  this  band  a 
series  of  bright  beads,  those  on  one  side  being  opposite  the  gaps 


Fig.  368. 

between  those  on  the  other  and  showing  that  the  brightest  point 
of  the  spark  alternated  between  the  knobs,  in  other  words,  the 
spark  passed  back  and  forth.  Knowing  the  rate  of  rotation  of 
the  mirror,  the  time  of  oscillation  of  the  spark  may  be  determined 
with  accuracy,  even  though  this  time  is  less  than  a  millionth  of  a 
second. 

689.  Explanation  of  Oscillation. — An  explanation  of  this  oscil- 
latory discharge  is  afforded  by  what  we  have  already  learned  of 
inductance.  Suppose  a  charge  to  be  given  to  the  jar  and  to  be 
gradually  increased  until  the  discharge  takes  place.  As  the  charge 
passes  from  the  inner  to  the  outer  coating  of  the  jar,  it  is  a  true 
current  and  the  inductance  of  the  circuit  causes  it  to  continue  to 
flow  beyond  the  point  when  the  jar  is  completely  discharged,  in 
other  words,  the  outer  coating  receives  an  excess  charge.  This 
then  flows  back  in  the  opposite  direction  and,  for  the  reason  given 
above,  the  inner  coating  now  acquires  an  excess  charge,  and  so  on. 
These  oscillations  do  not  continue  indefinitely  because  at  each  one 
a  portion  of  the  energy  is  spent  in  heating  the  circuit  and,  as  we 


HIGH  POTENTIAL  561 

shall  see  shortly,  another  portion  is  radiated  off  into  space.    The 
total  number  therefore  may  not  exceed  ten  or  twelve. 

Reflection  will  show  that  before  the  discharge  takes  place  the 
energy  of  the  field  is  electro-static,  that  is,  the  field  is  composed  of 
tubes  of  force  (Par.  62),  but  that  during  the  discharge  this  energy 
is  electro-magnetic,  the  conductor  being  surrounded  by  circular 
lines  of  force.  At  the  end  of  the  discharge  the  magnetic  lines  dis- 
appear and  the  tubes  of  force  reappear,  but  reversed  in  direction. 
As  the  return  oscillation  begins,  these  tubes  again  give  way  to 
magnetic  lines  of  force,  which  in  turn  are  in  reverse  direction  from 
the  first  set,  and  so  on. 

690.  Maxwell's  Electro- Magnetic  Theory.— In  1865  Maxwell 
published  a  mathematical  analysis  of  the  effects  produced  in  the 
surrounding  medium  by  an  oscillatory  discharge.  As  bases  for 
his  discussion  he  took  the  facts  (a)  that  a  current  flowing  in  a  con- 
ductor produces  about  the  conductor  a  magnetic  field,  (b)  that  if 
a  magnetic  field  about  a  conductor  be  varied,  an  E.  M.  F.  is  in- 
duced in  the  conductor,  (c)  that  the  electric  force  exerted  in  the 
space  about  a  charge  varies  inversely  with  the  dielectric  capacity 
and  (d)  that  the  magnetic  field  about  a  current  varies  with  the 
permeability  of  the  dielectric.  To  these  he  added  the  displace- 
ment assumption  which  is  that  when,  for  example,  a  charge  flows 
into  a  condenser,  an  equal  quantity  of  electricity  moves  in  the 
dielectric  between  the  plates,  but  that  this  movement  takes  place 
within  the  molecules  of  the  dielectric  and  not  from  one  molecule 
to  another.  The  effect  is  as  if  in  each  molecule  a  positive  charge 
had  moved  to  one  end,  a  negative  charge  to  the  other,  and  the 
positive  charged  ends  all  pointed  in  the  same  direction,  that  is, 
away  from  the  positive  plate  of  the  condenser.  The  so-called 
displacement  currents,  just  as  any  other  current,  produce  about 
them  a  magnetic  field. 

As  a  result  of  his  discussion  he  showed  that  these  oscillations 
give  rise  to  electric  waves  in  the  surrounding  space,  the  wave 
front  comprising  electric  displacements  and  magnetic  forces  at 
right  angles  to  each  other  and  both  at  right  angles  to  the  direction 
of  propagation  of  the  wave.  He  also  showed  that  these  waves 
moved  with  a  velocity  of  thirty  billion  centimeters  per  second. 
Since  light  moves  with  the  same  velocity  and  is  transmitted  by 
the  same  agent,  the  ether,  he  concluded  that  light  and  electricity 
are  identical  and  differ  only  in  that  the  light  waves  are  much  the 


562  ELEMENTS  OF  ELECTRICITY. 

shorter.  As  corroborating  this  last  conclusion,  he  showed  that 
since  electric  waves  can  not  be  transmitted  through  conductors, 
these  bodies  should  not  transmit  light  waves.  As  a  fact,  the 
metals  are  all  opaque  to  light.  The  same  reasoning  would  show 
that  a  transparent  solid  is  a  non-conductor  and  such  substances 
are  the  best  insulators.  It  does  not  follow  however  that  all  opaque 
bodies  are  conductors,  for  many,  such  as  porcelain,  marble,  etc., 
owe  their  opacity  to  irregular  crystallization  or  mechanically 
included  impurities.  The  purest  form  of  crystallized  marble, 
Iceland  spar,  is  transparent. 

Maxwell's  mathematical  discussion  can  not  be  repeated  here, 
but  by  following  a  similar  line  of  reasoning  we  show  in  the  three 
following  paragraphs  how  he  arrived  at  one  of  his  conclusions. 

691.  Electric  Elasticity.  —  The  elasticity  of  a  body  is  measured 
by  the  ratio  of  the  stress  exerted  upon  the  body  to  the  strain 
(elongation,  compression,  etc.)  produced.  Consider  a  sphere 
carrying  a  charge  Q  and  surrounded  by  a  concentric  non-con- 
ducting shell  of  dielectric  capacity  K.  Displacement  will  take 
place  in  the  dielectric,  a  charge  —  Q  being  induced  on  the  inner 
surface  of  the  shell  and  a  charge  +Q  being  repelled  to  the  outer 
surface.  If  the  radius  of  the  shell  be  r,  the  force  per  square  centi- 

meter exerted  upon  the  inner  surface  is  ^  •  ^  (Par.  90).    This  is 

the  stress  to  which  the  shell  is  exposed.  The  strain  per  square 
centimeter  consists  in  driving  the  positive  charge  to  the  outer  sur- 

face of  the  shell  and  is  therefore  ~-2.    The  electric  elasticity,  the 


ratio  of  the  stress  to  the  strain,  is  47r/  K. 

692.  Electric  Density.  —  In  Par.  435  there  was  deduced  an  ex- 
pression for  the  inductance  of  a  coil  wrapped  upon  a  circular  core. 
If  in  this  expression  both  /  and  L  be  absolute  electro-magnetic 
units  (instead  of  amperes  and  henrys),  the  expression  becomes 

T 
L= 


in  which  n  is  the  total  number 
of  turns,  r  is  the  radius  of  the  coil  and  I  is  its  length. 

In  Par.  687  it  was  shown  that  the  energy  of  an  electro-magnetic 
field  is  \PL.    Substituting  the  above  value  of  L  and  dividing 

2 


HIGH  POTENTIAL.  563 

by  7rr2l,  the  volume  of  the  core,  we  obtain  for  the  energy  per  cubic 
centimeter  ^ 

2MT 

If  for  n/l,  the  number  of  turns  per  centimeter,  we  write  Na 
this  becomes  l 


In  mechanics  it  is  shown  that  the  energy  of  a  mass  m  moving 
with  a  velocity  v  is  ^mv2.  From  analogy,  therefore,  kir^  is 
termed  the  electric  mass  per  unit  of  volume.  But  mass  per  unit 
volume  is  density,  therefore,  4^^  is  the  electric  density  of  the 
field. 

693.  Velocity  of  Propagation  of  Electric  Wave. — If  e  be  the 
elasticity  of  a  medium  and  6  be  its  density,  the  velocity  with 
which  waves  are  propagated  through  it  is  v  =  Ve/3.    Substitut- 
ing the  values  of  the  electric  elasticity  and  density  given  in  the 
preceding  paragraphs,  we  have  for  the  velocity  of  propagation 
of  electric  waves  1 

=  VK» 

This  is  the  expression  which  we  have  already  obtained  in  Par. 
548.  This  velocity,  by  many  independent  methods,  has  been 
shown  to  be  thirty  billion  (3xl010)  centimeters  per  second,  or 
as  already  stated,  the  same  as  the  velocity  of  light. 

694.  Hertz's    Confirmation    of    Maxwell's    Theory. — During 
Maxwell's  life  time  his  theory  made  but  moderate  headway  and 
he  died  before  it  had  ever  been  experimentally  proven.    In  1887, 
twenty-two  years  after  his  theory  had  been  announced,  it  re- 
ceived striking  and  abundant  confirmation  by  a  series  of  brilliant 
experiments  performed  by  Hertz.    The  arrangement  used  in  the 
first  of  these  experiments  is  shown  in  Fig.  369  and  consists  of 
two  parts  which  Hertz  designated  respectively  as  the  oscillator 
and  the  resonator.     The  oscillator  consisted  of  two  sixteen-inch 
square  zinc  plates,  A  and  B,  placed  two  feet  apart.    A  copper 
rod  from  each  of  these  and  upon  their  common  axis  terminated 
in  polished  knobs  separated  by  a  gap  G  of  about  one-quarter 
of  an  inch.    These  rods  were  connected  as  shown  to  the  terminals 
of  the  secondary  of  an  induction  coil.    When^the  coil  was  operated, 
series  of  sparks  passed  between  the  knobs.    The  resonator  con- 
sisted of  a  copper  wire  bent  into  a  circle  with  a  narrow  spark  gap 


564 


ELEMENTS  OF  ELECTRICITY. 


between  two  knobs.  It  was  found  that  to  obtain  the  best  results 
the  dimensions  of  the  resonator  had  to  be  adjusted,  or  it  had  to 
be  "tuned"  to  suit  the  particular  oscillator  used.  With  the  one 
described,  the  diameter  of  the  resonator  was  about  twenty- 
eight  inches. 


Fig.  369. 

With  the  coil  in  operation  and  sparks  passing  between  the 
knobs  of  the  oscillator,  the  resonator  was  held  in  various  near-by 
positions.  When  placed,  as  shown  in  the  figure,  along  the  line 
GM  passing  through  and  perpendicular  to  the  spark  gap  G,  it 
was  found  that  sparks  were  produced  in  the  gap  of  the  resonator 
whenever  the  axis  of  this  gap  was  parallel  to  the  spark  gap  of 
the  oscillator.  Thus  sparks  were  produced  when  the  resonator 
was  held  as  at  C  but  not  when  held  as  at  D  or  at  E. 

As  thus  carried  out,  this  experiment  does  not  conclusively 
show  the  existence  of  waves  and  might  be  considered  a  simple 
example  of  induction  as  explained  in  Par.  420.  The  demonstra- 
tion of  the  existence  of  waves  was  made  as  follows:  The  oscillator 
was  placed  so  that  its  axis  was  parallel  to  and  at  some  distance 
from  the  opposite  wall  of  the  room  in  which  the  experiments 
were  carried  out.  This  wall  was  covered  with  large  sheets  of 
zinc  M.  Since  according  to  Maxwell's  theory  the  metals  are 
opaque  to  these  waves,  this  zinc  sheet  should  act  towards  them 
as  a  mirror.  Now  it  is  well  known  that  when  waves  strike  a 
surface  normally  and  are  reflected  back  along  the  same  path, 
the  phenomenon  of  interference  occurs.  Beginning  at  the  re- 
flecting surface,  at  fixed  points  one-half  of  a  wave  length  apart 


HIGH  POTENTIAL.  565 

the  advancing  and  returning  waves  are  in  opposition  and  com- 
plete interference  results,  while  at  points  midway  between  these 
nodes  the  waves  are  in  phase  and  the  resulting  amplitude  is  twice 
that  of  the  advancing  wave.  With  the  resonator  close  to  the 
zinc  sheet  M,  no  sparks  are  obtained,  but  moving  from  M  towards 
G,  a  point  is  found  where  the  intensity  of  the  sparks  in  the  reson- 
ator is  a  maximum.  Continuing  to  move  towards  G,  the  sparks 
in  the  resonator  again  die  out,  then  again  rise  to  a  maximum. 
These  electro-magnetic  radiations  are  therefore  waves,  the  dis- 
tance between  two  successive  points  of  maximum  sparking  or 
between  two  nodes  of  no  sparking  being  one-half  of  the  wave 
length.  With  the  apparatus  described  above,  the  wave  length 
was  found  to  be  about  thirty-two  feet. 

By  the  method  just  outlined,  the  wave  length  can  be  deter- 
mined. By  photographing  the  spark  seen  in  the  revolving  mirror, 
the  periodic  time  of  the  oscillations  can  be  measured.  The  re- 
ciprocal of  this  is  the  frequency,  or  number  per  second.  The 
product  of  the  wave  length  by  the  frequency  gives  the  velocity 
with  which  the  wave  travels.  The  results  entirely  confirm  the 
previous  determinations  of  this  velocity  as  3xl010  centimeters 
per  second. 

695.  Further  Experiments  by  Hertz. — With  slight  modifica- 
tions in  his  simple  apparatus,  Hertz  succeeded  in  reproducing 
many  of  the  characteristic  experiments  usually  shown  with  light. 
Thus,  by  placing  the  spark  gap  of  his  oscillator  at  the  focus  of  a 
reflector  made  by  bending  a  sheet  of  zinc  into  a  parabolic  form, 
he  was  able  to  direct  the  waves  so  that  they  could  be  detected 
by  a  resonator  placed  at  the  focus  of  a  corresponding  reflector 
at  a  distance  of  over  thirty  yards.    By  using  a  huge  prism  of  pitch, 
four  feet  on  an  edge,  he  was  able  to  refract  the  beam  from  the 
parabolic  reflector.     Finally,  he  showed  that  these  waves  are 
polarized.    By  placing  in  the  path  of  the  beam  from  the  reflector 
a  screen  made  of  a  number  of  parallel  wires  strung  on  a  wooden 
frame,  he  showed  that  the  waves  pass  freely  when  the  wires 
were  perpendicular  to  the  axis  of  the  spark  gap  of  the  oscillator 
but  were  entirely  cut  off  when  these  wires  were  turned  so  as  to 
be  parallel  to  this  axis. 

696.  Length  of  Electro -Magnetic  Waves.— The  length  of  the 
longest  light  waves  is  a  little  over  .00007  of  a  centimeter,  while 


566  ELEMENTS  OF  ELECTRICITY. 

we  have  seen  above  that  that  of  the  electro-magnetic  waves 
produced  by  Hertz  in  his  first  experiment  was  thirty- two  feet. 
Since  the  velocity  of  these  waves  is  constant  and  is  equal  to  the 
product  of  the  wave  length  by  the  frequency,  and  since  the 
frequency  is  the  reciprocal  of  the  periodic  time,  the  wave  length 
varies  directly  with  the  periodic  time.  In  Par.  687  this  was  shown 
to  be  T  =  2irVLK,  therefore,  by  decreasing  either  the  inductance 
or  the  capacity  of  the  oscillator,  the  wave  length  may  be  shortened 
provided  the  condition  for  oscillatory  discharge,  R2  <  4L/  K  (Par. 
687)  be  maintained.  Since  all  conductors  have  both  inductance 
and  capacity,  Hertz  found  that  he  could  do  away  with  the  zinc 
plates  of  his  oscillator  and  substitute  for  them  simple  straight 
wires.  Other  investigators,  by  reducing  the  dimensions  of  the 
oscillator,  have  produced  electro-magnetic  waves  whose  length 
has  been  about  two-tenths  of  a  centimeter. 

697.  Tuning  of  the  Resonator. — By  experiments  based  upon 
several  different  principles  it  has  been  shown  that  electric  oscil- 
lations may  also  be  transmitted  along  wires. 

Consider  a  length  of  insulated  wire  and  suppose  an  electric 
impulse  to  be  applied  to  it.  The  wave  produced  will  travel  the 
length  of  the  wire  and  having  reached  the  far  end  will  be  reflected 
and  return.  If  on  its  way  back  it  encounters  another  wave 
traveling  in  the  opposite  direction,  the  two  waves  will  combine. 
If  they  be  in  phase,  the  amplitude  of  the  resultant  wave  is  doubled 
and  would  be  further  increased  by  each  successive  wave.  If  they 
be  in  opposition,  they  mutually  destroy  one  another  and  complete 
interference  results.  Between  these  extremes,  recurring  risings 
and  fallings  result  and  produce  an  effect  analogous  to  the  "beats" 
in  sound  waves.  If  the  waves  be  of  constant  length,  the  time 
required  for  them  to  travel  to  the  end  of  the  wire  and  return 
varies  with  the  length  of  the  wire.  It  is  therefore  possible  by 
lengthening  or  shortening  the  wire  to  adjust  it  so  that  the  wave 
will  return  in  exact  time  to  receive  the  maximum  increment 
from  the  succeeding  impulse.  When  this  adjustment,  the  tuning 
referred  to  in  Par.  694,  has  been  made,  the  waves  in  the  wire 
are  of  maximum  intensity  and  resonance  is  said  to  have  been 
secured. 

As  an  analogy,  a  pendulum  has  a  natural  period  of  vibration. 
If  successive  impulses  be  applied  to  the  pendulum  and  be  timed 
at  its  natural  period,  their  effects  are  cumulative  and,  although 


HIGH  POTENTIAL.  567 

the  individual  impulses  may  be  very  feeble,  they  may  finally 
produce  motion  through  a  wide  arc.  If,  on  the  other  hand,  they 
be  not  timed  at  this  period,  little  or  no  oscillation  will  be  pro- 
duced. 

Reflection  will  show  that  resonance  may  be  obtained  in  another 
way,  that  is,  by  varying  the  length  of  the  wave  instead  of  varying 
the  length  of  the  circuit.  It  was  shown  in  the  preceding  paragraph 
how  this  may  be  done  by  varying  the  periodic  time.  There  are, 
therefore,  two  ways  of  obtaining  resonance  in  a  resonator:  (a)  by 
shortening  or  lengthening  the  resonator  and  thus  changing  its 
natural  period  to  suit  the  period  of  the  waves  and  (b)  by  vary- 
ing the  period  of  the  waves  to  suit  the  natural  period  of  the 
resonator. 

698.  Principle  of  Wireless  Telegraphy. — Hertz  showed  by  his 
experiments  that  there  could  be  produced  at  will  electric  waves 
which  travel  through  space  with  the  velocity  of  light.    He  also 
showed  that  by  suitably-arranged  apparatus  these  waves  could 
be  detected  at  a  distance  from  their  point  of  origin.     It  was 
quickly  realized  that  these  two  observations  comprised  the  funda- 
mental principle  of  wireless  telegraphy.    Subsequent  development 
has  taken  place  along  two  lines:  (a)  the  improving  of  the  sending 
apparatus  or  oscillator  so  that  a  greater  amount  of  energy  could 
be  thrown  out  in  the  form  of  waves,  and  (b)  the  perfecting  of  the 
receiving  apparatus,  increasing  its  sensitiveness  so  that  the  waves 
could  be  detected  at  greater  and  greater  distances.     Foremost 
among  those  engaged  in  these  problems  was  Marconi  who  in 
1895  took  out  his  first  patents  on  methods  of  wireless  telegraphy. 

In  order  to  bring  out  clearly  the  object  of  the  various  parts 
of  the  modern  apparatus,  we  shall  describe  the  simpler  forms 
and  show  why  changes  were  found  desirable. 

699.  The  Aerial. — The  primary  form  of  apparatus  for  pro- 
ducing electric  waves  was  the  oscillator  of  Hertz.     As  stated 
above,  it  was  soon  discovered  that  the  zinc  plates  could  be  re- 
placed by  straight  wires.    It  was  next  found  that  if  these  wires 
be  placed  in  a  vertical  position  instead  of  horizontal,  that  the 
lower  one  could  be  dispensed  with,  the  earth  taking  its  place. 
In  either  case,  the  length  of  the  waves  produced  remained  the 
same,  that  is,  a  little  over  four  times  the  length  of  the  upper  wire. 
To  this  vertical  wire  the  names  aerial  or  antenna  are  applied. 


568  ELEMENTS  OF  ELECTRICITY. 

With  other  conditions  constant,  the  distance  to  which  signals 
can  be  sent  varies  as  the  square  of  the  length  of  the  aerial  and 
for  this  reason  Marconi  at  first  proposed  that  it  should  be  sup- 
ported by  kites  or  balloons.  This  proposition  was  found  to  be 
impracticable  for  permanent  installations  and  antennae  are  now 
supported  by  towers  or  masts. 

The  signaling  distance  also  increases  directly  with  the  amount 
of  energy  radiated.  In  Par.  97  it  was  shown  that  the  energy 

of  a  condenser  is    ^V2K,  K  being  its  capacity.     In  this  case 

the  aerial  and  the  grounded  wire  and  the  earth  below  the  spark 
gap  constitute  the  condenser.  We  may  therefore  increase  its 
capacity  by  increasing  the  length  of  the  aerial,  but,  as  shown 
above,  the  practical  limit  of  length  is  soon  reached.  The  next 
solution  therefore  is  to  add  to  the  capacity  by  using  a  number 
of  wires  in  the  aerial.  The  capacity  of  a  single  wire  is  consider- 
able. Pierce  states  that  a  straight  wire  f  inch  in  diameter  and 
100  feet  long  has  the  same  capacity  as  an  isolated  metallic  disc 
16  feet  in  diameter.  If,  however,  more  than  one  wire  be  used, 
owing  to  the  mutual  action  of  the  like  charges  which  they  carry, 
the  capacity  is  far  from  increasing  in  proportion  to  the  number 
of  wires,  in  fact,  it  increases  more  nearly  as  the  square  root  of 
this  number,  that  is,  sixteen  wires  two  feet  apart  have  only  four 
times  the  capacity  of  a  single  wire. 

700.  The  Transmitter. — A  simple  form  of  transmitter  is  shown 
diagrammatically  in  Fig.  370.  A  is  the  aerial  and  D  is  the  lower 
wire  grounded  at  E.  B  is  a  battery  in  circuit  with  the  primary 
of  an  induction  coil  C.  The  terminals  of  the  secondary  are  con- 
nected to  A  and  D  on  opposite  sides  of  the  spark  gap  G.  When 
the  key  K  is  closed,  the  E.  M.  F.  induced  in  the  secondary  drives 
a  charge  into  A  until  a  spark  jumps  across  G,  thereby  producing 
the  desired  electrical  oscillations. 

We  saw  above  that  the  signaling  distance  increases  directly 
with  the  amount  of  energy  radiated  and  we  also  saw  that  the 

energy  of  a  condenser  is  ^  V2K.    The  signaling  distance  therefore 

varies  with  two  factors,  K,  the  capacity,  and  V2,  the  square  of 
the  potential  in  the  aerial.  The  capacity  may  be  increased  by 
increasing  the  number  of  wires  in  the  aerial,  but,  as  shown  above, 
this  increase  is  far  from  being  in  proportion  to  the  number  of 
wires  added.  The  most  promising  method  is  to  increase  the 


HIGH  POTENTIAL. 


569 


difference  of  potential  across  G.  This  can  be  done  by  separating 
the  knobs  more  widely,  for,  in  order  to  throw  a  spark  across  this 
wider  gap,  the  aerial  must  be  charged  to  a  higher  potential. 
This  solution,  however,  involves  another  difficulty  for  as  we 
widen  the  gap  G,  we  greatly  increase  the  resistance  and  we  have 
seen  that  in  order  that  the  oscillations  may  be  produced  by  the 
spark,  R2  must  be  less  than  ±L/K  (Par.  687).  If,  therefore,  R 
be  increased  too  much,  the  discharge  is  no  longer  oscillatory. 


Fig.  370. 

701.  Coupled  Circuits. — There  still  remains  a  way  by  which 
the  potential  in  the  aerial  may  be  increased  without  increasing 
the  resistance  across  the  spark  gap.  This  is  by  applying  to  the 
oscillatory  circuit  the  principle  of  the  step  up  transformer.  One 
form  of  this  arrangement  is  shown  diagrammatically  in  Fig.  371. 
The  battery,  key  and  induction  coil  are  just  as  described  above 
but  in  addition  there  is  shunted  around  the  spark  gap  G  a  circuit 
containing  a  condenser  D  (usually  a  battery  of  Ley  den  jars), 
and  a  coil  F.  This  coil  is  the  primary  of  an  air  core,  step  up  trans- 
former, the  secondary  of  which  is  the  coil  H  in  series  with  the 
aerial  AE.  In  the  actual  apparatus,  the  coil  H  is  within  the  coil 
F,  although  separated  from  it  by  considerable  space.  For  the 
sake  of  clearness  they  are  represented  in  the  diagram  as  entirely 
separate.  When  the  key  K  is  closed,  the  high  voltage  of  the 
secondary  of  C  causes  the  condenser  D  to  receive  a  large  charge 


570 


ELEMENTS  OF  ELECTRICITY. 


and  therefore  when  a  spark  occurs  at  G,  a  large  current  oscillates 
back  and  forth.  As  this  current  flows  through  F,  it  induces  a 
corresponding  oscillatory  current  in  H,  the  voltage  of  this  last 
being  greater  than  that  in  F  in  proportion  to  the  ratio  of  the 
number  of  turns  in  H  to  those  in  F.  The  voltage  in  the  aerial 
is  therefore  stepped  up  and  the  waves  which  it  sends  forth  have 
so  much  the  more  energy. 


Fig.  371. 

The  arrangement  just  described  is  said  to  be  inductively- 
coupled.  Sometimes  F  and  H  are  parts  of  one  continuous  coil, 
that  is,  they  constitute  an  auto-transformer  (Par.  652).  In  this 
case  the  apparatus  is  said  to  be  direct-coupled.  Owing  to  the 
very  high  frequency  of  the  oscillations,  hysteresis  prevents  the 
use  of  iron  cores  in  these  coils. 

Commercial  wireless  telegraph  plants  no  longer  employ  the 
battery  and  induction  coil  as  described  in  the  preceding  paragraphs 
but  use  alternating  current  generators  of  from  2  to  5  kilowatts 
capacity  and  supplying  220  volts  at  500  cycles.  The  current 
from  these  generators  is  stepped  up  by  suitably-designed 
transformers. 

702.  Tuning  of  Coupled  Circuits.— The  aerial  (Fig.  371)  has 
a  natural  period,  that  is,  there  is  an  electric  wave  of  a  certain 
length  which  will  produce  in  it  resonance.  If  the  waves  in  the 
circuit  FD  can  be  made  of  this  length,  resonance  will  be  set  up  in 
the  aerial  and  it  will  radiate  a  maximum  amount  of  energy. 
This  circuit  contains  capacity  in  the  shape  of  the  condenser  D, 


HIGH  POTENTIAL.  571 

and  inductance  in  the  coil  F.  In  Par.  696  it  was  shown  that  the 
length  of  a  wave  in  an  oscillatory  circuit  varies  as  2nr\/LK',  we 
may  therefore  vary  the  wave  length  by  varying  either  the  induc- 
tance or  the  capacity  or  both.  Condensers  of  variable  capacity 
are  of  frequent  use  for  this  purpose.  In  the  diagram,  however, 
the  inductance  is  represented  as  variable.  The  wire  from  D  to  F 
connects  to  F  by  means  of  a  clip  and  may  be  slid  up  or  down  so 
as  to  embrace  fewer  or  more  turns  of  the  coil.  To  determine 
when  resonance  is  secured,  a  hot  wire  ammeter  (Par.  463)  is  in- 
serted in  the  aerial  either  above  or  below  H  and  the  inductance 
of  F  is  varied  until  the  ammeter  shows  a  maximum  current. 

703.  Branley's  Coherer. — Having  seen  how  electric  waves  may 
be  produced,  we  shall  now  show  how  they  may  be  detected  at 
a  distance. 

The  receiving  circuit,  like  the  transmitter  already  described, 
has  an  aerial,  in  fact,  by  means  of  a  shifting  switch  uses  the  same 
aerial  as  the  transmitter  at  the  same  station.  The  waves  from  a 
distance  strike  this  aerial  and  produce  in  it  electrical  oscillations, 
but  these  are  usually  very  feeble.  The  first  efforts  were  therefore 
directed  to  produce  a  sensitive  relay  (Par.  412)  which  would 
operate  under  these  feeble  oscillations  and  close  a  delicate  switch, 
thereby  throwing  in  on  some  recording  apparatus  an  auxiliary 
source  of  current. 

A       B 


CM: 


Fig.  372. 

The  first  successful  solution  of  this  problem  was  made  by  a 
device  due  to  Branley.  In  1890  he  found  that  metallic  filings 
placed  between  two  metal  plugs  in  a  glass  tube,  the  plugs  consti- 
tuting the  terminals  of  an  electric  circuit,  were  ordinarily  non- 
conductive  or  at  least  of  very  high  resistance,  but  were  rendered 
conductive  by  electric  oscillations  in  their  vicinity.  If,  after 
being  so  rendered  conductive,  the  filings  were  jarred,  their  original 
high  resistance  was  restored.  No  entirely  satisfactory  explana- 
tion of  this  phenomenon  has  been  given.  His  discovery  resulted 
in  a  piece  of  apparatus,  the  coherer,  which  in  the  hands  of  Marconi 
took  the  form  shown  in  Fig.  372.  It  consists  of  a  slender  glass 
tube  in  which  are  two  metal  plugs  A  and  B  separated  by  a  nar- 


572 


ELEMENTS  OF  ELECTRICITY. 


row  space  in  which  are  loosely  piled  rather  coarse  filings  of  a 
mixture  of  95  parts  nickel  and  5  parts  silver.  The  wires  connect- 
ing with  the  plugs  are  sealed  into  the  tube  and  the  tube  itself  is 
then  exhausted  and  sealed.  The  exhaustion  of  the  tube  is  to  pre- 
vent the  filings  from  becoming  tarnished. 

704.  Operation  of  Receiving  Circuit. — The  operation  of  the 
receiving  circuit  will  be  understood  from  the  following:  The  in- 
coming electric  waves  produce  oscillations  in  the  aerial  A  (Fig. 
373)  which  render  the  coherer  a  conductor.  This  enables  the 


Fig.  373. 

battery  B  to  send  a  current  through  the  coherer  and  the  relay. 
This  current  is  very  feeble,  being  less  than  one-thousandth  of  an 
ampere,  but  is  sufficient  to  cause  the  relay  to  operate  and  thus 
throw  in  the  battery  C  on  the  Morse  sounder,  or  on  whatever 
recording  apparatus  may  be  used  in  its  place.  It  also  throws 
this  battery  in  on  the  buzzer  D,  an  apparatus  identical  in  operation 
with  the  bell  described  in  Par.  410.  The  small  hammer  of  this 
buzzer  beats  against  the  coherer,  jarring  the  filings  sufficiently 
to  cause  them  to  decohere  and  restoring  the  resistance  of  the 
coherer  so  that  it  is  in  readiness  to  receive  the  next  succeeding 
oscillations.  These  oscillations,  however,  in  trains  of  ten  or 
twelve  (Par.  689),  follow  each  other  with  such  rapidity  that  the 
relay  is  kept  closed  and  the  sounder  does  not  release  its  armature 
until  the  operator  at  the  sending  station  opens  his  key.  The 
sounder  therefore  repeats  the  dots  and  dashes  made  at  the  send- 
ing key. 

705.  Use  of  Telephone  and  Detectors. — The  relay  and  coherer 
as  described  above  have  given  way  to  much  more  sensitive  forms 


HIGH  POTENTIAL. 


573 


of  receiving  apparatus  with  corresponding  increase  in  signaling 
distance. 

In  place  of  the  relay,  sensitive  telephones  are  now  employed. 
Pierce  states  that  while  it  requires  about  1/200  of  a  volt  to  operate 
a  relay,  a  540  cycle  alternating  E.  M.  F.  of  8  millionths  of  a  volt 
will  produce  an  audible  sound  in  such  a  telephone. 

Instead  of  the  coherer,  many  more  sensitive  forms  of  detectors 
have  been  devised.  These  are  of  a  number  of  classes,  only  two 
of  which  we  shall  mention. 

In  1896  General  H.  H.  C.  Dunwoody  (Class  of  1866,  U.  S.  M.  A.) 
discovered  that  a  crystal  of  carborundum  (Par.  488)  inserted  in 
an  electric  circuit  served  as  a  detector  of  electric  oscillations. 
Many  other  crystalline  substances,  such  as  sulphide  of  molyb- 
denum, oxide  of  zinc,  silicon,  etc.,  have  since  been  found  to 
possess  the  same  property.  Pierce  by  some  beautifully  conceived 
and  brilliantly  performed  experiments  has  shown  that  the  action 
of  the  crystals  is  to  rectify  the  oscillatory  currents  in  some  way 
analogous  to  the  operation  of  the  mercury  arc  rectifier  (Par.  654). 
He  therefore  designates  them  as  "crystal  rectifiers." 

Their  operation  may  be  understood  from  the  following:  In  the 
diagram  (Fig.  374),  A  represents  a  metal  point  pressing  upon  a 
crystal  B,  and  T  is  a  telephone  shunted  around  AB.  Suppose 
that  the  oscillatory  currents  in  the  aerial  may  pass  upward 
through  AB  but  not  downward  (although 
this  direction  is  immaterial).  The  suc- 
cessive oscillations  follow  at  intervals 
which  may  be  less  than  a  millionth  of  a 
second,  and  the  currents  flowing  upward 
but  not  downward,  a  charge  accumulates 
in  the  antennae.  When  the  oscillations 
cease,  this  charge  flows  down  through  the 
telephone.  The  extreme  rapidity  of  the 
oscillations  prevent  them  from  causing 
vibrations  in  the  diaphragm  of  the  tele- 
phone, and  even  if  they  did  cause  such 
vibrations,  their  frequency  would  be  far 
beyond  anything  that  the  ear  can  detect. 
The  downward-flowing  charges  however  follow  in  accordance 
with  the  intervals  between  the  sparks  at  the  sending  station,  and 
thus  produce  an  audible  note. 


574  ELEMENTS  OF  ELECTRICITY. 

Fessenden  has  devised  an  electrolytic  detector  which  also  has  been 
shown  to  be  a  rectifier.  It  differs  from  the  arrangement  shown  in 
Fig.  374  in  that  B  is  a  small  platinum  cup  containing  dilute  acid, 
and  A  is  a  platinum  wire,  a  thousandth  of  an  inch  or  less  in  diame- 
ter and  barely  touching  the  acid  in  B.  There  is  also  inserted  in 
the  telephone  circuit  a  single  cell  which  sends  a  feeble  but  steady 
current  through  the  telephone.  The  oscillatory  current  in  the 
aerial  causes  the  current  through  the  telephone  to  vary  and  thus 
produce  a  sound. 

706.  Tuning  of  Receiving  Circuits. — The  receiving  circuit  is 
not  quite  so  simple  as  represented  in  Fig.  374  but  is  usually  a 
coupled  circuit  (Par.  701)  and  contains  both  a  variable  condenser 
and  a  variable  inductance.    By  varying  one  or  both  of  these,  the 
circuit  may  be  adjusted  so  as  to  be  in  resonance  with  the  parti- 
cular waves  which  are  being  received.    If  waves  of  different  lengths 
are  arriving,  the  circuit  may  be  tuned  to  resonance  with  those  of 
one  length  to  the  exclusion  of  those  of  other  lengths.    This  natur- 
ally suggests  that  where  two  wireless  stations  are  endeavoring  to 
communicate  and  are  being  disturbed  by  signals  from  other 
stations,  confusion  may  be  avoided  and  perhaps  privacy  secured 
if  by  pre-arrangement  the  two  stations  concerned  should  use 
waves  of  different  lengths  from  those  used  by  the  other  stations. 
This  involves  the  ability  of  the  stations  to  ascertain  the  length  of 
wave  which  they  are  emitting  and  to  adjust  their  apparatus  to 
emit  waves  of  the  desired  length.    This  information  is  furnished 
by  several  forms  of  wave  meters,  instruments  carrying  a  graduated 
scale  from  which,  when  they  have  been  adjusted  to  resonance, 
may  be  read  direct  the  length  of  the  corresponding  wave  in  the 
exciting  circuit. 

The  standard  wave  length  now  used  in  communicating  with 
vessels  at  sea  is  425  meters. 

707.  Distance  Attained  by  Wireless  Telegraphy. — The  distance 
to  which  wireless  signals  may  be  sent  is  constantly  being  increased 
and  with  more  powerful  sending  apparatus,  loftier  antennae  and 
more  sensitive  receiving  instruments,  there  appears  to  be  no  reason 
why  eventually  they  may  not  be  exchanged  between  diametri- 
cally opposite  points  on  our  globe.    Within  the  present  year  (1913) 
signals  have  been  exchanged  between  the  station  at  Arlington, 
Virginia,  and  Gibraltar,  Panama  and  Alaska. 


HIGH  POTENTIAL.  575 

Several  theories  have  been  advanced  to  explain  why  it  is  pos- 
sible to  send  these  signals  around  considerable  arcs  of  the  earth's 
circumference.  According  to  some,  the  radiations  proceed  in 
straight  lines  but  at  a  height  of  about  50  miles  in  the  atmosphere 
reach  a  point  where  the  pressure  is  so  reduced  that  the  air  is  a 
conductor  just  as  in  the  Geissler  tubes  (Par.  670).  Since,  as  we 
have  already  seen  (Par.  690),  these  waves  can  not  penetrate  a 
conductor,  they  are  reflected  from  this  tenuous  stratum  and  thus 
by  successive  reflections  pass  around  the  arc. 

According  to  others,  the  waves  leave  the  grounded  aerial  and 
slide  along  over  the  surface  of  the  earth  like  an  immense  inverted 
U.  The  better  the  conducting  surface,  the  better  the  transmis- 
sion of  the  waves.  This  is  corroborated  by  the  fact  that  signals 
can  be  exchanged  at  a  much  greater  distance  over  salt  water  than 
over  land. 

Finally,  it  is  a  fact  not  yet  explained  that  these  signals  can  be 
sent  nearly,  if  not  quite,  twice  as  far  at  night  as  they  can  during 
the  day  and  that  the  conditions  for  attaining  long  distance  are 
especially  unfavorable  at  sun  rise  and  at  sun  set. 


INDEX. 


577 


INDEX. 

References  are  to  Paragraphs. 


Absolute  measurement  of  current, 
374,  546 

of  resistance,  542,  546 
Absolute  temperature,  256 
Absolute  unit  of  current,  355,  536,  546 

of  E.  M.  F.,  426,  537 

of  electric  power,  496 

of  resistance,  427,  546 

of  self-induction,  433 
Absolute  zero  of  temperature,  289 
Accumulator,  237 

chloride,  241 

reactions,  244 
Acheson,  488 
Actinium,  679 

Adaptation  of  generator  to  w,ork,  582 
Adjustment  of  mariner's  compass,  183 
Advantages  of  electro-magnet,  405 

of  multipolar  machines,  574,  639 

of  Edison  battery,  253 
Aerial,  699,  701,  702 
Aging  of  magnets,  167 
Air,  dielectric  strength  of,  93 
Air  condenser,  86,  87 
Alpha  rays,  679 
Alternating  current,  554,  606 

compared  with  direct,  656 

graphic  representation  of,  555,  618, 
627 

rectification  of,  556,  653 

transformation  of,  648 

value  of,  612,  613 
Alternating  current  motors,  657 

classes  of,  658 

Alternating  E.  M.  F.,  graphic  repre- 
sentation, 555,  618,  627 

composition  of,  611 
Alternation,  608 
Alternator,  compound,  638 

di-phase,  644 


Alternator,  field  excitation  of,  637 

inductor,  640,  643 

polyphase,  640,  644,  645 

single  phase,  640,  644 

tri-phase,  645,  646,  647 
Alternators,  636,  649 

classes  of,  640 

usually  multipolar,  639 

with  revolving  armatures,  641 

with  revolving  field,  642 
Aluminum,  manufacture  of,  489 
Amber,  12 

American  telegraph  system,  413 
Ammeter,  455, 457,  459,  467,  471, 472, 
474,  702 

classes,  462 

connection  of,  457,  459 

millivoltmeter  as,  474 

resistance  of,  457,  459 

Weston,  D.  C.,  467 
Ammeter  shunt,  465,  466 
Amount  of  induced  charge,  31 
Ampere,  181,  344,  345,  346,  360,  371 
Ampere  defined,  228,  232,  307,  448,, 

544,  546 

Amperes,  virtual,  612 
Ampere  turns,  388 
Analogues  of  electric  potential,  70 
Analogy  between  cells  and  pumps,  33S 
Angle  of  lag,  609 

of  lead,  570,  60 
Anode,  220 
Antenna,  699 
Apparent  power,  635 
Application  of  electrolysis,  233,  234, 

235 

Arago,  428 
Arc,  electric,  485 

enclosed,  521 

flaming,  522 


578 


INDEX. 


Arc  lamp,  515 

constant  current,  520 

constant  potential,  519 

magnetite,  523 
Arc  lamp   mechanism,   requirements 

of,  517 

Arc  lights,  efficiency,  524 
Armature,  124,  560 
Armature  core,  560,  565 
Armature  reaction,  570,  587 
Armatures,  classes  of,  566 
Arrhenius,  dissociation  theory  of,  268 
Artificial  magnets,  109 
Astatic  combination,  366,  368 
Atomic  character  of  electricity,  280, 

685 

Attracted  disc  electrometer,  101,  102 
Attraction,  electric,  15,  16,  17,  30 

magnetic,  112,  120 
mutual,  114 
takes  place  through  intervening 

bodies,  113 

Auto-transformer,  652,  701 
Avogadro's  law,  256 
Ayrton,  381,  445,  454 
Back  E.  M.  F.,  297,  593,  594,  595 
Balance,  Coulomb's  torsion,  52,  100, 

127,  132 

Ballasting  coil,  508,  519,  527 
Ballistic  galvanometer,  384 
Base,  electrolysis  of,  223 
Battery  defined,  191 

De  La  Rive's  floating,  370 

development  of  power  in,  49 

lead,  care  of,  248 
objections  to,  249 
troubles  of,  247 

storage,    charging,    245,   246,   415, 

582 

Bauxite,  489 
Becquerel  rays,  679,  680 
Bell,  electric,  410 
Bell  telephone,  440 
Beta  rays,  679 
Bichromate  cell,  205 
Bifilar  suspension,  127,  382 
Biot's  experiment,  39 
Bipolar  generator,  561 


Blow  out,  magnetic,  485 
Bolometer,  534 
Boys,  Vernon,  534 
Branley,  703 
Bridge,  meter,  325 

slide  wire,  325 

Bridge,  Wheatstone,  arrangement  of 
resistances,  315 

evolution  in  form,  316 

measurement  of  resistances  by,  317, 
318,  319,  320,  321 

principle  of,  313,  314 

resistances  measured  by,  324 

with  reversible  ratios,  322 
Brushes,  553,  560,  568 

shifting  of,  570,  571,  598 
Brush  holders,  568 
Bunsen's  cell,  204 
Bus  bars,  579 
Buzzer,  704 
C.  G.  S.  system,  10 
Calcium  carbide,  manufacture  of,  488 
Calculation  of  E.  M.  F.  of  generator, 
578 

of  flux  of  magnetic  circuit,  401 
Calibration  of  galvanometer,  454 
Calorie,  11,  478 
Canal  rays,  676 
Candle  power,  509 
Capacity,  79,  607,  625 

E.  M.  F.  and  current  curves  in  case 
of,  627 

of  plate  condenser,  89 

of  sphere,  80 

of  spherical  condenser,  88 

of  wires,  699 

practical  unit  of,  95 

and  resistance,  629 

inductance  and  resistance,  630 
Capacity,  electric,  45,  79,  83,  88,  95 
Capacity,  dielectric,  31,  90,  92 

determination  of,  91 
Capacity  reactance,  628 
Carbon,  variation  of  resistance  with 
pressure,  285 

with  temperature,  289 
Carbons  for  arc  lamps,  516 
Carbon  filament,  505 


INDEX. 


579 


Carborundum,  manufacture  of,  488 

use  as  detector  in  wireless,  705 
Care  of  lead  batteries,  248 
Cathode,  220 
Cathode  rays,  671,  672,  680 

effect  of  electric  field  on,  674 

effect  of  magnetic  field  on,  673 
Cell,  bichromate,  205 

Bunsen's,  204 

Clark's  standard,  212 

conventional  sign  for,  214 

Daniell's,  206,  427,  544,  546 

defined,  201 

dry,  210 

Edison-Lalande,  208 

electrolytic,  220 

elements  of,  193,  194 

gravity,  207 

Grove's,  203 

Leclanche,  209 

Plante,  240 

primary,  201 

secondary,  237,  238 

simple,  193 

chemical  action  in,  195 
dissociation   theory    applied   to, 
279 

standard,  need  of,  211 

Weston's  standard,  213 

voltaic,  requirements  of,  200 
Cells,  191 

analogy  with  pumps,  338 

classification  of,  202 

E.  M.  F.  of,  200 

great  variety  of,  201 

grouping  of,  334 

in  multiple,  339 

in  parallel,  336,  337 

in  series,  335,  337 

internal  resistance  of,  294 

reversibility  of,  236 
Centimeter,  7 
Characteristic  defined,  583 

external,  585 

internal,  585 

magnetization,  584 

of  series  generator,  585 

of  shunt  generator,  587 


Charge,  bound,  33 

carried  by  corpuscle,  675 

confined  to  surface,  38,  39,  68 

distribution  of,  40 

division  of,  45 

electric,  18 

free,  33 

induced,  amount  of,  31 
distribution  of,  29 

of  storage  battery,  indications  of, 
246 

on  conductor,  37,  68 

on  non-conductor,  36 

on  surface  exerts  no  force  on  in- 
terior point,  67 

residual,  87 

surface  density  of,  41,  65,  66 
Charges,  induced,  separation  of,  32 

variation  of  electric  force  with,  54 
Charging  Edison  battery,  252 

storage  battery,  245,  246,  582 

from  A.  C.,  655,  656 
Charles'  law,  256 
Chart,  isoclinic,  173 

isodynamic,  174 

isogonic,  170 

Chemical  action  in  simple  cell,  195 
Chloride  accumulator,  241 

reactions,  244 
Choke  coil,  621,  622,  650 
Circlet  of  cups,  Volta's,  191 
Circuit,  no  current  unless  complete, 
216 

divided,  293 

division  of  current  in,  300 
Circular  coil,  field  at  center,  354 

field  on  axis  of,  354 
Circular  measure  of  wires,  296 
Circular  mil,  296 
Clark's  standard  cell,  212 
Classes  of  A.  C.  motors,  658 

of  alternators,  640 

of  armatures,  566 

of  D.  C.  motors,  598 

of  electrical  machines,  550 
Classification  of  ammeters  and  volt- 
meters, 462 

of  cells,  202 


580 


INDEX. 


Clutch  for  arc  lamps,  518 
Coercive  force,  398 
Coherer,  703,  704 
Coil,  choke,  621,  622,  650 

induction,  438 
use  of  condenser  with,  439 

resistance,  311 

rotating  in  magnetic  field,  551 
Collector  rings,  553 
Commercial   unit   of  electric  power, 
496 

of  electric  work,  496 
Commutation,  556,  571 
Commutation  plane,  570 
Commutator,  556,  560,  567 
Commutator  segments,  567 
Comparison  of  A.  C.  and  D.  C.,  656 
Compass,  mariner's,  182 

adjustment  of,  183 
Composition  of  alternating  E.  M.  F.s, 

611 
Compound  alternator,  638 

generator,  563,  588 
Condenser,  83,  86,  94,  96 

energy  of,  97 

in  A.  C.  circuit,  626 

location  of  charge  in,  87 

use  with  induction  coil,  439 

work  expended  in  charging,  96 
Condenser,  plate,  capacity  of,  89 

spherical,  capacity  of,  88 
Conditions    affecting   wireless    teleg- 
raphy, 707 
Conductance,  292 
Conductivity,  292 

of  gases,  667,  680 
Conductor  defined,  19 
Conductors  and  non-conductors,  19 

table  of,  20 

Conductors   carrying  currents,  force 
exerted  between,  361,  362 

in  parallel,  resistance  of,  293 

in  series,  resistance  of,  286 
Connection  of  transformers,  651 
Consequent  poles,  165 
Constant  current  arc  lamp,  520 
Constant  potential  arc  lamp,  519 
Contact  series,  Volta's,  187 


Contact  theory,  Volta's,  188 
Control  of  field  of  machines,  564 

of  light,  513 

of  speed  of  shunt  motor,  600 
Controlling  force,  146 

method  of  weakening,  366 
Conventional  sign  for  cell,  214 
Converter,  rotary,  653 

synchronous,  653 
Cooper-Hewitt,  527 
Copper,  refining  by  electrolysis,  233 
Core  of  armature,  560,  565 

of  solenoid,  effect  upon  field,  390 
Core  transformer,  649 
Corpuscles,  672,  681,  682,  685 

mass  of,  684 

nature  of  charge  carried  by,  675 

velocity  of,  683 

Cost  of  power  from  primary  cells,  343 
Coulomb,  38,  42,  52,  53,  100, 123, 128, 

132 
Coulomb,  the,  56,  228,  536 

defined,  228 
Coulomb's  first  law,  115,  123 

second  law,  128,  133 

torsion  balance,  52,  100,  127,  132 
Counter  E.  M.  F.,  297,  593 

in  motor,  593,  594 

reading  of  voltmeter  across,  595 
Coupled  circuits,  701,  702 
Coupling  of  generators,  581 
Critical  frequency,  631 

resistance,  586 
Crookes,  671 
Crookes'  dark  space,  670 

tube,  670,  671,  672,  675,  676,  677, 

678,  682 
Cryolite,  489 
Crystal  rectifiers,  705 
Gumming,  529 
Curie,  679 

Current,  absolute  unit  of,  355,  356, 
536,  546 

alternating,  value  of,  612,  613 

direction  of  flow  of,  217 

displacement,  690 

division  in  divided  circuit,  300 

eddy,  428 


INDEX. 


581 


Current — Continued. 

electric,  215 
effects  of,  215,  444 
mechanical  production  of,  423 
work  done  by,  476 

equality  at  every  cross  section,  229 
I  Foucault's,  429 

measurement   of,  by  tangent   gal- 
vanometer, 374 

none  unless  circuit  complete,  216 

practical  unit  of,  228,  307,  448,  546 

production  by  rotating  coil,  553 

rotation  by  magnetic  pole,  351 

units  of,  536 

Curves  of  magnetization,  394 
Cutting  of  lines  of  force,  424,  425 
Cycle,  608 

of  magnetization,  398 
Cylinder  machine,  48 
D.  C.  generator,  essential  parts,  560 
Daniell's  cell,  206,  423,  427,  544,  546 
Damping,  electrical,  379,  430,  467,  471 
D'Arsonval  galvanometer,  378,  467 
Davy,  223,  270,  515 
Dead  beat  instruments,  379 
Declination,  annual  change  in,  179 

diurnal  change  in,  178 

magnetic,  169,  177 

secular  change  in,  177 
Decomposition,  chemical,  257 

of  water,  218 
Deflection  of  needle,  right  hand  rule 

for,  345 

De  La  Rive's  floating  battery,  370 
Delta  connection,  646 
Density,  electric,  692 
Depolarizers,  199 
Detector,  crystal,  705 

electrolytic,  705 
Detectors  in  wireless  telegraphy,  703, 

704,  705 
Detonator,  483 
Diagrams,  electric,  5~ 

of  parallel  series  grouping,  342 

vector,  610 
Dial  bridge,  323 
Diamagnetics,  122 
Diamagnetism,  122,  402 


Dielectric,  55 

Dielectric  capacity,  31,  90,  92 

determination  of,  91 
Dielectric  coefficient,  90 
Dielectric  strength,  93 
Dimensional    formula   of   resistance, 
540 

formulae,  539,  547 

table  of,  547 

Difference  of  potential,  69,  73 
Dip,  magnetic,  171,  177 

secular  change  in,  177 
Di-phase  alternator,  644 
Dipping  needle,  172 
Direct  coupling,  701 
Direct  current  compared  with  alter- 
nating, 656 

transformation  of,  648 
Direct  current  motors,  classes,  598 
Direction  of  electric  field,  59,  61 

of  field  about  wire  carrying  a  cur- 
rent, 347,  348 

of  flow  of  current,  217 

of  rotation  of  motor,  604 
Discharge  through  high  vacua,  670 

through  moderate  vacua,  668 
Discovery  of  Galvani,  185 
Displacement  current,  690 
Dissociation,  257 

by  heat,  258 

extensive  scope  of  theory  of  elec- 
trolytic, 281 

theory  applied  to  simple  cell,  279 

theory  of  Arrhenius,  268 
Distance  attained  by  wireless  teleg- 
raphy, 707 

Distribution  of  induced  charge,  29 
Divided  circuit,  293 

division  of  current  in,  300 

drop  of  potential  in,  312 
Division  of  charge,  45 
Drop  of  potential,  298,  299 

in  divided  circuit,  312 

measurement  of  resistance  by,  309, 

310 

Drum  winding,  plane  development  of» 
576 

star  development  of,  577 


582 


INDEX. 


Drum  wound  armature,  566,  575,  576, 

577 

Dry  cell,  210 
Dunwoody,  705 
Dynamo,  550 
Dynamotor,  605 
Dyne,  11 
E.  M.  F.,  absolute  unit  of,  426,  537 

counter,  297,  593 
in  motor,  593,  594 

;:     power  of  motor  proportional  to, 

594 
reading  of  voltmeter  across,  595 

depends  on  rate  of  cutting  of  lines 
of  force,  425 

induced  at  make  and  break,  437 

measurement  by  voltmeter,  461 

of  cells,  200 

measurement  of,  329 

of  generator,  578 

of  rotating  coil,  552 

power,  617 

produced  by  cutting  lines  of  force, 
425 

reactive,  619 

thermo-electric,  528 

units  of,  537 
E.  M.  F.s,  alternating,  composition 

of,  611 

Earth  a  magnet,  116 
Earth's  magnetic  poles,  location  of, 

168 

Earth's  magnetism,  theories  of,  181 
Earth's  poles  misnamed,  117 
Eddy  current,  428 
Edison,  504 

Edison-Lalande  cell,  208 
Edison  storage  battery,  250 

advantages  and  disadvantages,  253 

charging,  252 

reactions,  251 
Effect  of  points,  42,  43 
Effects  of  electric  current,  215,  444 
Efficiency  of  arc  lights,  524 

of  incandescent  lamp,  512 

of  mercury  vapor  lamp,  527 

of  motors,  596 

of  transformers,  649 


Elasticity,  electric,  691 
Electric  arc,  485 

attraction  and  repulsion  explained, 
30 

laws  of,  24 
bells,  410 

capacity,  45,  79,  83,  88,  95 
charge,  18 

cause  of  movement,  69 
current,  215 

effects  of,  215 

magnetization  by,  164 

mechanical  production  of,  423 

work  done  by,  476 
density,  692 
diagrams,  51 
elasticity,  691 
field,  57,  58,  59,  61,  65,  66 

effect  on  cathode  rays,  674 

graphic  representation  of,  61 

intensity  of,  58,  61 

unit,  58,  61 
force,  54,  55,  58,  75 

variation  with  charges,  54 

variation  with  intervening  medi- 
um, 55,  58 

furnace,  486,  497,  490,  491 
fuze,  483 

heating  of  wires,  480,  481 
light,  503 

lines  of  force,  60,  61 
pendulum,  22 
potential,  70,  72,  73,  74,  75,  83 

analogues  of,  70 

how  measured,  72 
power,  absolute  unit  of,  49 

commercial  unit  of,  496 

expression  for,  494 

measurement  of,  497,  498 

practical  unit  of,  496 
primer,  483 
repulsion,  22 
resonance,  63 
telegraph,  411 
waves,  690,  694 

length  of,  696 

velocity  of  propagation,  693,  694 
welding,  484 


INDEX. 


583 


Electric  whirl,  44 

wind,  42,  44,  48,  49,  50 
work,  commercial  unit  of,  496 
Electrical   effects   used   in   measure- 
ments, 444,  445,  446 
energy,  source  of  in  cell,  192 
machines,  46,  47,  48,  49,  50 

classes  of,  550 

transmission  of  power,  501,  502 
Electricity,  atomic  character  of,  280, 

685 

origin  of  name,  12 
static,  14 
theories  of,  27 
two  kinds,  26 
unit  quantity  of,  56 
Electrification,  all  bodies  susceptible 

of,  21 

by  influence,  28 
resinous,  23 
two  kinds  of,  23 
vitreous,  23 
Electro-chemical  classification  of  the 

elements,  225 
Electro-chemical  effect  standard  for 

measurements,  448 
unsuited  for  commercial  measure- 
ments, 451 
Electro-chemical  equivalent  defined, 

231 

Electro-chemical  rectifier,  653 
Electro-dynamics,  360 
Electro-dynamometer,    measurement 

of  power  by,  498 
Siemen's,  383 
Weber's,  382 
Electro-magnet,  403 
lifting  weights  by,  409 
rule  for  polarity,  404 
shape  of,  407 
use  of,  408 
value  of,  405 

Electro-magnetic  effect  used  in  meas- 
urements, 452,  453 

Electro-magnetic    field,    energy    ex- 
pended upon,  359 
inertia  of,  418 


Electro-magnetic  induction  explained, 

419,  420 

Electro-magnetic  inertia,  418 
Electro-magnetic  theory  of  light,  548, 

690,  694 

Electro-magnetic  intensity,  535 
Electro-magnetic  units,  primary,  538 
Electro-mechanics,  549 
Electro-static  units,  535 
Electrode,  220 

Electrolysis,  applications  of,  233,  234, 
235 

Faraday's  terminology  of,  220 

of  a  base,  223 

of  fused  compound,  222 

of  a  salt,  224 

of  water,  219 

substances  subject  to,  221 
Electrolyte,  193,  220 
Electrolytes  and  non-electrolytes,  275 
Electrolytes,  measurement  of  resist- 
ance of,  327 
Electrolytic  cell,  220 

detector  of  wireless,  705 
Electrolytic     dissociation,     extensive 

scope  of  theory,  281 
Electrolytic  properties  depend  upon 

ionization,  276 
Electrometer,  attracted  disc,  101,  102 

quadrant,  103,  104 
Electrometers,  principle  of,  100 
Electro-motive  force,  76,  77,  78  (see 
E.  M.  F.) 

practical  unit  of,  77 
Electrons,  280,  672,  685 
Electrophorus,  35 
Electroplating,  234 
Electropoion  fluid,  205 
Electroscope,  25 

gold  leaf,  34,  680 
Electrostatic  measurements,  98 
Electrotyping,  235 

Elements,  electro-chemical  classifica- 
tion of,  225 

magnetic,  175 
variation  of,r!76 

of  a  cell,  193,  194 

of  a  secondary  cell,  238 


584 


INDEX. 


Enclosed  arc,  521 

Energy,  electrical,  source  of  in  cell,  192 
expended  upon  an  electro-magnetic 

field,  359 

loss  due  to  hysteresis,  399 
of  a  condenser,  97 

Equality  of  current  at  every  cross  sec- 
tion of  circuit,  229 
Equation,  Helmholtz's,  436 
Equipotential  surface,  71,  72 
Equivalent,  electro-chemical  defined, 

231 

^rg,  11 

Essential  parts  of  D.  C.  generator,  560 
Ewing,  153,  359,  399 
Ewing's  theory  of  magnetism,  153,  359 
Exceptions  to  Van't  Hoff's  generaliza- 
tion, 267 

Excitation  of  field  magnets,  562 
Exciter,  637,  656 

Explanation  of  motion  of  motor,  591 
Expression  for  electric  power,  494 
for  inductance  of  coil,  435 
for  permeability,  392 
External  characteristic,  585 
Fables  of  ancients  concerning  mag- 
nets, 107 

Factor,  power,  635 
Farad,  95 
Faraday,  31,  38,  55,  91,  122,  181,  220, 

226,  230,  416,  417 
Faraday  dark  space,  670 
Faraday's  discovery  of  induction,  416, 

417 

first  law,  226 
ring  transformer,  431 
second  law;  230 

terminology  of  electrolysis,  220 
Feddersen's  experiment  with  revolv- 
ing mirror,  688 
Fessenden,  705 

Field  at  center  of  circular  coil,  354 
electric,  57,  58,  59,  61,  65,  66 
direction  of,  59,  61 
effect  on  cathode  rays,  674 
graphic  representation  of,  61 
intensity  of,  58 
near  uniformly-charged  plane,  66 


near  uniformly-charged  sphere,  65 
unit,  58 

Field,    electro-magnetic,    energy    ex- 
pended upon,  359 
inertia  of,  418 

intensity  of,  about  a  straight  con- 
ductor, 353 
Field,  magnetic,  about  a  wire  carrying 

a  current,  346 
direction  of,  347,  348 
defined,  134 
determination  of  strength  of,  148, 

149,  150 
direction  of,  135 
effect  on  cathode  rays,  673 
effect  on  positive  column,  669 
graphic  representation  of  intensity 

of,  145 

intensity  of,  136 

Field  of  electrical  machines,  143,  561 
of  generator,  561 
of  solenoid,  effect  of  material  of  core 

upon,  390 

variation  with  current,  389 
on  axis  of  circular  coil,  354 
on  axis  of  solenoid,  387 
rotary,  production  of,  664          [147 
Fields,  magnetic,  comparison  of,  146, 

compounding,  141 
Field  coils,  561 
Field  control,  564 
Field  excitation  of  alternators,  673 
Field  magnets,  561 

excitation  of,  562,  673 
Filament,  carbon,  505 
Flaming  arc,  522 
Fleming,  292 

Flow  of  current,  direction  of,  217 
Fluoroscope,  678 
Flux,  calculation  of,  401 
law  of  maximum,  144 
magnetic,  142 
Focusing  tube,  678 
Force,  coercive,  398 
electric,  75 

variation  with  charges,  54 
variation  with  intervening  me- 
dium, 55,  58 


INDEX. 


585 


Force,  electric  lines  of,  60,  63,  64 
from  unit  charge,  63 

electromotive,  76,  77,  78  (see  E.  M. 
F.) 

exerted  between  conductors  carry- 
ing currents,  361,  362 

exerted   by   field   upon   conductor 
carrying  a  current,  356 

exerted  on  internal  point  of  charged 
body,  67 

magneto-motive,  400 

tubes  of,  62 

unit  of,  11 

Forces,  magnetic,  measurement  of,  127 
Formula,  dimensional,  of  resistance, 

540 

Formulae,  dimensional,  539,  547 
Foucault,  429,  515 
Foucault's  currents,  429 
Franklin,  27,  43,  86 
Franklin's  fulminating  pane,  86 

theory  of  electricity,  27 
Free  charge,  33 

Free  ions,  demonstration  of,  272 
Free  magnetism,  142 
Frequency,  608 

critical,  631 

Frictional  machines,  46,  47,  48 
Furnace,  electric,  486,  487,  490,  491 

induction,  491 

Moissan's,  487 
Fuse,  306,  481 

Fused  compound,  electrolysis  of,  222 
Fuze,  electric,  483 
Galvani,  185 
Galvani's  discovery,  185 
Galvanometer,  ballistic,  384 

calibration  of,  454 

D'Arsonval,  378 

defined,  372 

mirror,  377 

reflecting,  378 

sine,  376 

suspended  coil,  378 

tangent,  373,  546 
Galvanometer  constant,  374 
Galvanometer  shunts,  need  of,  380 


Galvanoscope  defined,  363 

increase  of  sensitiveness,  364 

methods  of  weakening  controlling 

force  of,  366 
Gambey,  428 
Gamma  rays,  679 
Gases,  conductivity  of,  667,  680 

ionization  of,  681 
Gaseous  pressure,  laws  of  variation  of, 

256 

Gauges,  wire,  295 
Gauss,  11,  64,  148 
Gauss'  theorem,  64 
Geissler  tube,  670 
Generator,  adaptation  to  work,  582 

and  motor  identical,  590 

calculation  of  E.  M.  F.,  578 

compound,  563,  588 

ring  wound,  569 

series,  563,  582 

characteristic  of,  585 

shunt  wound,  563,  582 
characteristic  of,  587 
Generators,  423,  550,  560,  561,  563 

classes  of  D.  C.,  563 

coupling  of,  581 

used  in  wireless  telegraphy,  701 
Gilbert,  12,  108,  110,  116,  117,  121, 

156,  158,  159,  168 
Gold  leaf  electroscope,  34,  680 
Gram,  8 

Gravity  cell,  207 
Gray,  Stephen,  19 
Grid,  239 

Grotthus'  theory,  274 
Grouping,  mesh,  646 

of  cells,  334 

of  incandescent  lamps,  514 

of  storage  battery  plates,  243 

star,  647 
Grove's  cell,  203 
Hauy's  method,  366,  367 
Heat,  dissociation  by,  258 

effect  on  magnetization,  158 

unit  of,  11,  478 

Heating  effect,  laws  of,  477,  478 
Heating  effect  of  current,  localizing, 
482 


586 


INDEX. 


Heating,  electric,  of  wires,  480,  481 

Hefner,  the,  509 

Helmholtz,  280 

Helmholtz's  equation,  436 

Henry,  the,  433,  434 

Henry,  Professor,  403,  686 

Henry's  theory  of  oscillatory  discharge 

of  condenser,  686 
Hertz,  694,  695,  696,  697,  698 
Hertz's    confirmation    of    Maxwell's 
theory,  694,  695 

oscillator,  694,  699 

resonator,  694 
High  potential,  666 
High  resistance,  measurement  of,  326 
Hopkinson,  392 
Holtz's  influence  machine,  50 
Horse  power,  494 
Hot  wire  instruments,  463,  702 
Hysteresis,  396 

energy  loss  due  to,  399 
Impedance,  620 
Incandescent  lamp,  504 

control  of  light  of,  513 

efficiency  of,  512 

life  of,  511 

Incandescent  lamps,  grouping  of,  514 
Inclination,  magnetic,  171 
Inclined  coil  instruments,  471 
Increase  in  number  of  coils  of  gener- 
ator, 558 
Increase  in  number  of  turns  of  coil  of 

generator,  557 
Increase  of  sensitiveness  of  galvano- 

scopes,  364 

Indicating  wattmeter,  499 
Indication  of  charge  of  storage  bat- 
tery, 246 
Induced  charge,  amount  of,  31 

distribution  of,  29 
Induced  charges,  separation  of,  32 
Induced  E.  M.  F.  at  make  and  break, 
437 

rule  for  direction  of,  421,  422 
Inductance,  434,  615,  619 

and  resistance  contrasted,  616 
effect  of  alternating  E.  M.  F.,  617 
in  parallel,  624 


Inductance  and  resistance  in  series, 

623 
Inductance,  resistance  and  capacity, 

630 

Inductance  of  coil,  expression  for,  435 
Induction,  electro-static,  28,  30 
Induction,  electro-magnetic,  explained, 
419,  420 

Faraday's  discovery  of,  416,  417 

magnetic,  takes  place  through  space, 
119 

magnetization  by,  118 

self,  432,  614 

measure  of,  433 
Induction  coil,  438 

use  of  condenser  with,  439 
Induction  furnace,  491 
Induction  motor,  428,  662,  663,  664, 

665 

Inductive  coupling,  701 
Inductive  reactance,  619 
Inductor,  560,  569 
Inductor  alternator,  640,  643 
Inertia,  electro-magnetic,  418 
Influence,  electrification  by,  28 
Influence  machines,  46,  49,  50 
Instruments,  hot  wire,  463 

inclined  coil,  471 

moving  iron,  464 
Integrating  wattmeter,  500 
Intensity,  magnetic,  174 

of  electric  field,  58,  61 

of  field  about  a  straight  conductor, 
353 

of  force  between  conductors  carry- 
ing current,  362 
Internal  characteristic,  585 
Internal  resistance  of  cells,  294 

measurement  of,  328 
International  ohm,  291 
International  volt,  212 
Interrupter,  410,  438 
Intrinsic  magnetism,  142 
Inverse  squares,   experimental  proof 
of  law,  131,  132 

law  of,  53 

Inversion,  thermo-electric,  529 
Investigations  of  Volta,  186 


INDEX. 


587 


lonization,  268 

electrolytic  properties  depend  upon, 
276 

how  it  takes  place,  270 

incomplete,  271 

of  gases,  681 

why  it  takes  place  in  solutions,  269 
Ions,  220,  681 

free,  demonstration  of,  272 

not  from  same  molecule,  273 
Iron-clad  magnet,  409 
Iron  furnace,  electric,  490 
Isoclinic  chart  and  lines,  173 
Isodynamic  chart  and  lines,  174 
Isogonic  chart  and  lines,  170 
Jars,  unit,  99 
Joint  resistance,  293 
Joule,  477,  478 
Joule,  the,  478 
Joule's  law,  478,  479 
Kelvin,  Lord,  102,  103,  377,  529,  531, 

687 

Kirchoff's  laws,  303,  304 
Lag,  angle  of,  609 
Laminated  magnets,  166    • 
Lamp,  arc,  515 

constant  current,  520 

constant  potential,  519 

magnetite,  523 
Lamp,  incandescent,  504 

control  of  light,  513 

efficiency  of,  512 

life  of,  511 

manufacture  of,  506 
Lamp,  mercury  vapor,  527 

Nernst,  508 

tantalum,  507 

tungsten,  507,  512 

Lamps,  incandescent,  grouping  of,  514 
Lamps,  luminous  vapor,  525,  526,  527 
Lap  winding,  575 
Laplace,  353,  361 
Law,  Avogadro's,  256 

Charles',  256 

Coulomb's  second,  128,  133 

Faraday's  first,  226 

Faraday's  second,  230 

Joule's,  478,  479 


Law,  Laplace's,  361 

Lenz's,  430 

Mariotte's,  256 
osmotic  pressure  follows,  264 

Maxwell's,  144,  371,  377,  467,  470, 
471,  591 

of  bifilar  suspensions,  127 

of  inverse  squares,  53 

experimental  proof  of,  131,  132 

of  magnetic  circuit,  400 

of  maximum  flux,  144 

of  torsion,  52,  127 

Ohm's,  297,  299,  307,  427,  538 

sine,  147 

tangent,  146 
Laws,  Kirchoff's,  303,  304 

of  heating  effect,  477,  478 

of  resistance,  285,  286,  287,  288,  289 

of  variation  of  gaseous  pressure,  256 
Lead,  angle  of,  570,  609 
Lead  batteries,  care  of,  248 

objections  to,  249 

troubles  of,  247 
Leclanche  cell,  209 
Left  hand  rule  for  direction  of  motion 

of  current,  352 
Lenard  rays,  677,  680 
Length,  standard  of,  4 

unit  of,  7 

Length  of  electric  waves,  696 
Lenz's  law,  430 
Leyden  jar,  85,  86,  87,  103 

Feddersen's  proof  of  oscillatory  dis- 
charge, 688 

invention  of,  84 

oscillatory  discharge  of,  686,  689 

Thomson's  proof  of  oscillatory  dis- 
charge, 687 

Lichtenberg's  figures,  36 
Life  of  incandescent  lamp,  511 
Light,  electric,  503 
Lifting  power  of  magnets,  124 
Lightning  rod,  43 
Lines,  isoclinic,  173 

isodynamic,  174 

isogonic,  170 
Lines  of  force,  cutting  of,  424,  425 

electric,  60,  61,  63,  64 


588 


INDEX. 


Lines  of  force,  from  unit  charge,  63 

magnetic,  137 

method   of   mapping,    138,    139, 

141 
pass  preferably  through  magnetic 

substances,  143 
properties  of,  142,  143 
Local  action,  196 

remedy  for,  197 
Localizing  heating  effect  of  current, 

482 
Location  of  earth's  magnetic   poles, 

168 

Lodestones,  106,  159 
Lost  volts,  305 

Luminous  vapor  lamps,  525,  526,  527 
Machines,  electrical,  46,  47,  48,  49,  50 

classes  of,  550 
Magnet,  origin  of  name,  105 

the  earth  a,  116 

tractive  power  of,  406 

turning  moment  of,  149 
Magnets,  aging  of,  167 

artificial,  109 

fables  of  ancients  relating  to,  107 

laminated,  166 

lifting  power  of,  124 

most  suitable  metal  for  making,  160 

mutual  action  of,  115 

natural,  105 

principle  of  manufacture,  161 

strength  of,  125 
Magnet  cores,  561 
Magnet,  electro,  403 
Magnetic  attraction,  112 

explained,  120 

mutual,  114 

takes    place    through    intervening 

bodies,  113 

Magnetic  blowout,  485 
Magnetic  circuit,  law  of,  400 
Magnetic  declination,  169 
Magnetic  dip,  171 
Magnetic  elements,  175 

variation  of,  176    . 
Magnetic  field  about  wire  carrying  a 
current,  346,  347,  348 

coil  rotating  in,  551 


Magnetic  field,  defined,  134 

determination  of  strength  of,  148, 
149,  150 

direction  of,  135 

effect  on  cathode  rays,  673 

effect  on  positive  column,  669 

force  exerted  upon  conductor  car- 
rying a  current,  356 

graphic  representation  of  intensity 
of,  145 

intensity  of,  136 

Magnetic  fields,  comparison  of,  146, 
147 

compounding,  141 
Magnetic  figures,  138,  139,  140,  141 

use  of,  140 
Magnetic  flux,  142 
Magnetic  force,  115,  123 
Magnetic  forces,  measurement  of,  127 
Magnetic  inclination,  171 
Magnetic  intensity,  174 
Magnetic  lines  of  force,  137,  143 

methods  of  mapping,  138,  139,  141 

pass  preferably  through  magnetic 
substances,  143 

properties  of,  142,  143 
Magnetic  maps,  170 
Magnetic  meridian,  168 
Magnetic  moment,  130 
Magnetic  needle,  polarity  of,  116 
Magnetic  pole  defined,  126 

unit,  133 
Magnetic  poles,  110 

inseparable,  111 
Magnetic  saturation,  393 
Magnetic  screen,  113,  143 
Magnetic  shell,  369 
Magnetic  storms,  180 
Magnetic  substances,  121 
Magnetic  variation,  169 
Magnetism,  151 

earth's,  theories  of,  181 

Ewing's  theory  of,  153,  395 

free,  142 

intrinsic,  142 

molecular,  152,  395 

Tesidual,  155,  398,  562 
Magnetite  arc  lamp,  523 


INDEX. 


589 


Magnetization  accompanied  by  molec- 
ular movement,  154 
by  divided  touch,  163 
by  double  touch,  163 
by  electric  current,  164 
by  induction,  118,  570 
by  single  touch,  162 
characteristic,  584 
confined  to  outer  layers  of  magnet, 

166 

curves  of,  394 
cycle  of,  398 
effect  of  heat  on,  158 
facilitated  by  molecular  movement, 

155 

facilitated  by  solution,  159 
facilitated  by  vibration,  156 
loss  facilitated  by  vibration,  157 
Magneto-motive  force,  400 
Make  and  break,  induced  E.  M.  F. 

at,  437 

Manganin,  289 

Manufacture  of  aluminum,  489 
of  calcium  carbide,  488 
of  carborundum,  488 
of  electric  lamps,  506 
of  magnets,  162,  163,  164 

principle  of,  161 
Mapping  magnetic  lines  of  force,  138, 

139,  141 

Maps,  magnetic,  170 
Marconi,  698,  699,  703 
Mariner's  compass,  182 

adjustment  of,  183 
Mariotte's  law,  256 

osmotic  pressure  follows,  264 
Mass,  unit  of,  8 

of  corpuscles,  684 
Maximum     current     from    multiple 

grouping,  340 

Maximum  flux,  law  of,  144 
Maximum  output  of  power  by  motor, 

597 
Maxwell's  displacement  assumption, 

690 
electro-magnetic  theory  of  light,  548, 

690,  694 
law,  144, 371,  377, 467, 470, 471,  591 


Maxwell's    theory,    confirmation    by 

Hertz,  694,  695- 

Mean  spherical  candle  power,  509 
Measure  of  self  induction,  433 
Measurement,   absolute,   of   current, 

374 

of  resistance,  542,  546 
Measurement  of  current  by  tangent 

galvanometer,  374,  546 
of  E.  M.  F.  by  voltmeter,  461 
of  E.  M.  F.  of  cells,  329,  461 
of  electric  power,  497,  498,  635 
of  high  resistance,  326 
of  internal  resistance  of  cells,  328 
of  magnetic  forces,  127 
of  osmotic  pressure,  261 
of  power  by  electro-dynamometer, 

498 

of  resistance,  308 
by  drop  of  potential,  309,  310 
by  Wheatstone  bridge,  317,  318, 

319,  320,  321 

of  resistance  of  electrolytes,  327 
with  potentiometer,  332 
Measurements,  electrical  effects  used 

in,  444,  445,  446, 
electro-chemical  effect  standard  for, 

448 
electro-chemical  effect  unsuited  for 

commercial  needs,  451 
electro-magnetic  effect  used  in,  452, 

453 

electro-static,  98 
Mechanical  potential,  71 
Mechanical   production  of  electrical 

current,  423 
Medium,   variation  of  electric  force 

with  intervening,  55,  58 
Mercury  arc  rectifier,  654,  655 
Mercury  vapor  lamp,  527 
Meridian,  magnetic,  168 
Mesh  grouping,  646 
Metal,    most    suitable    for    making 

magnets,  160 
Meter  bridge,  325 
Method  by  oscillations,  129,  131 
of  weakening  controlling  force  of 
galvanometers,  366 


590 


INDEX. 


Methods  of  self-excitation,  563,  638 
Metric  system,  6 
Microhm,  288 
Mil  foot,  296 
Millivoltmeter,  473 

as  ammeter,  474 
Millivoltmeter  shunt,  475 
Mirror  galvanometer,  377 
Moissan's  furnace,  487 
Molecular  magnetism,  152,  395 
Molecular  movement  facilitates  mag- 
netization, 155 

magnetization  accompanied  by,  154 
Molybdenite  as  detector  for  wireless, 

705 

Moment,  magnetic,  130 
Moore  light,  526 
Morse,  411 
Morse  alphabet,  412 

telegraph,  412 
Motor,  550 

direction  of  rotation  of,  604 

efficiency  of,  596 

explanation  of  motion,  591 

identical  with  generator,  590 

induction,  428,  662,  663,  664,  665 

maximum  output  of  power  by,  597 

power  developed  by,  592 

power  proportional  to  counter  E. 
M.  F.,  594 

repulsion,  662 

series,  602 
for  A.  C.,  659 
speed  of,  603 

shunt,  599  _ 

control  of  speed  of,  600 

synchronous,  660 

operation  of,  661 
Motors,  alternating  current,  657 

classes  of,  658 

classes  of  D.  C.,  598 
Motor  generator,  605,  648,  653 
Moving  iron  instruments,  464 
Multiple  grouping  of  cells,  339 
Multiplier,  469 

Schweigger's,  365 
Multipolar  alternator,  639 
Multipolar  generator,  561,  578 


Multipolar  generators,  advantages  of, 

574,  639 

Natural  magnets,  105 
Nature  of  corpuscles,  685 
Needle,  dipping,  172 

magnetic  polarity  of,  116 
Negative  electricity,  674 
Negative  glow,  670 
Negative  ions,  672 
Nernst,  278 
Nernst  lamp,  508,  512 
Neutral  plane,  551,  570 
Neutral  temperature,  529 
No  field  release,  601 
No  voltage  release,  601 
Norman,  Robert,  171 
Objections  to  lead  batteries,  249 
Observations  of  Pfeffer,  262,  263 
Oerstedt's  discovery,  344,  363 
Ohm,  the,  284,  543,  546 

defined  in  terms  of  column  of  mer- 
cury, 291,  543 

international,  291,  543 
Ohm's  law,  297,  299,  307,  538 
Open  and  closed  coils,  559 
Operation  of  synchronous  motors,  661 

of  telephone,  442 

of  transformer,  650 
Oscillations,  method  by,  129,  131 
Oscillator,  694 

Oscillatory  discharge  of  Ley  den  jar, 
686,  689 

Feddersen's  proof  of,  688 

Thomson's  proof  of,  687 
Osmosis,  259 
Osmotic  pressure,  259 

demonstration  of,  260 

follows  Mariotte's  law,  264 

measurement  of,  261 

variation  of,  263,  264,  265,  266 
Ostwald,  272 
Overcompounding,  589 
Overload  switch,  306,  414 
Parallel  grouping  of  cells,  336,  337 

diagrams,  342 
Parallel-series  grouping,  339 

diagrams,  342 
Paramagnetics,  122 


INDEX. 


591 


Peltier  effect,  530 
Pendulum,  electric,  22 
Period,  608 
Permeability,  391,  397 

expression  for,  392 
Pfeffer,  observations  of,  262,  263 
Phase,  609 
Phase  difference,  609 
Photometry,  510 
Pierce,  699,  705 
Pile,  voltaic,  190 
Pitch  blende,  679 
Plane  development  of  drum  winding, 

576 

Plante  cell,  240 

Plates,  storage  battery,  dimensions  of, 
242 

grouping  of,  243 

preparation  of,  239 
Platinum  thermometer,  290 
Points,  effect  of,  42,  43 

experiments  with,  43,  44 
Polarity  of  electro-magnet,  rule  for, 

404 

Polarization,  198 
Pole,  magnetic  defined,  126 

rotation  by  current,  350 

unit,  133,  535 
Poles,  consequent,  165 

earth's,  location  of,  168 
misnamed,  117 

magnetic,  110 

inseparable,  111 
Polonium,  679 

Polyphase  alternators,  640,  644,  645 
Positive  column,  668 

effect  of  magnetic  field  upon,  669 
Positive  rays,  676 
Potential  at  point  due  to  a  charge,  74 

difference,  73 

drop  of,  298,  299 

electric,  70,  72,  73,  74,  75,  83 
analogues  of,  70 
how  measured,  72 

mechanical,  71 

zero,  73 
Potentiometer,  arrangement  of,  330 

calibration  of,  331 


Potentiometer,  forms  of,  333 

measurement  with,  332 
Power,  apparent,  635 
defined,  492 

developed  by  motor,  592 
development  in  a  battery,  495 
electric,  absolute  unit  of,  496 
commercial  unit  of,  496 
expression  for,  494 
measurement  of,  497,  498,  635 
practical  unit  of,  496 
transmission  of,  501,  502,  656 
from  primary  cells,  cost  of,  343 
in  A.  C.  circuit,  634 
maximum  output  by  motor,  597 
measurement   of,  by  electro-dyna- 
mometer, 498 
of  motor  proportional  to  counter 

E.  M.  F.,  594 
tractive,  of  magnet,  406 
Power  E.  M.  F.,  617 
Power  factor,  635 
Practical  unit  of  capacity,  95 
of  current,  228,  307,  448,  546 
of  E.  M.  F.,  427 
of  electric  power,  496 
of  quantity,  228 
of  resistance,  284,  546 
of  self  induction,  433,  434 
Preparation  of  plates  of  storage  bat- 
tery, 239 
Pressure,  variation  of  resistance  with, 

285 

gaseous,  laws  of  variation,  256 
osmotic,  259 
demonstration  of,  260 
follows  Mariotte's  law,  264 
measurement  of,  261 
variation  of,  263,  264,  265,  266 
Primary  cell,  201,  202 

cost  of  power  from,  343 
Primary  electro-magnetic  units,  538 
Prime  conductor,  47 
Primer,  electric,  483 
Principle  of  electrometers,  100 
of  induction  motor,  663 
of  tangent  galvanometer,  375 
of  wireless  telegraphy,  698 


592 


INDEX. 


Production  of  current  by  rotating  coil, 
553 

of  rotating  field,  664 
Proof  plane,  38 
Quadrant  electrometer,  103 

theory  of,  104 

Quantity,  electro-static  unit  of,   56, 
535 

units  of,  536 
Radio-activity,  679 
Haftometer,  533 
Radio-micrometer,  534 
Radium,  679 
Rays,  alpha,  679 

Becquerel,  679,  680 

beta,  679 

canal,  676 

cathode,  671,  672,  680 

effect  of  electric  field  on,  674 
effect  of  magnetic  field  on,  673 

gamma,  679 

Lenard,  677,  680 

positive,  676 

Rontgen,  678 

X,  678,  679,  680,  684 
Reactance,  capacity,  628 

inductive,  619 

Reaction,  armature,  570,  587 
Reactions    of    chloride    accumulator, 
244 

of  Edison  battery,  251 
Reactive  E.  M.  F.,  619 
Receiving  circuit  for  wireless,  704 

tuning  of,  706 

Recording  wattmeter,  499,  500 
Rectification  of  A.  C.,  556,  653 

of  single  phase  current,  655 
Rectifier,  crystal,  705 

electro-chemical,  653 

mercury  arc,  654,  655 
Reflecting  galvanometer,  378 
Relay,  412,  703,  704,  705 

sensitiveness  of,  705 
Reluctance,  391,  400 

specific,  400 
Reluctivity,  400 
Remedy  for  local  action,  197 
Repulsion,  electric,  22,  30 


Repulsion  motor,  662 

Requirements  of  arc  lamp  mechanism, 

517 

of  voltaic  cell,  200 
Residual  charge,  87 
Residual  magnetism,  155,  398,  562 
Resistance,  292 

absolute  measurement  of,  542 
absolute  unit  of,  427,  546 
critical,  586,  587 
defined,  282 

dimensional  formula  of,  540 
example  of  effect  of,  283 
expressed  as  a  velocity,  541 
internal,  of  cells,  294 

measurement  of,  328 
joint,  293 

laws  of,  285,  286,  287,  288,  289 
measurement  of,  308 

by  drop  of  potential,  309,  310 
by  Wheatstone  bridge,  317,  318, 

319,  320,  321 

of  conductors  in  parallel,  293 
of  conductors  in  series,  286 
of  electrolytes,  measurement  of,  327 
of  voltmeter,  458,  459,  460,  461, 

468 

practical  unit  of,  284,  546 
Siemen's  unit  of,  543 
specific,  285,  288 
temperature  coefficient  of,  289 
variation   with   temperature,    285, 

289 

Resistance  and  capacity,  629 
Resistance  and  inductance  contrasted, 

616 
effect    on    alternating    E.    M.    F., 

617 
Resistance  and  inductance  in  parallel, 

624 

in  series,  623 
Resistance,  inductance  and  capacity, 

630 
Resistances,  arrangement  of,  in  bridge, 

315 

measurable  by  bridge,  324 
Resistance  coils,  311 
Resistivity,  292 


INDEX 


593 


Resonance,  631,   632,  633,  697,  702, 

706 
with  inductance  and   capacity  in 

parallel,  633 
with  inductance  and  capacity  in 

series,  632 
Resonator,  694 

tuning  of,  697 
Retentivity,  155 

Reversible  ratios,  bridge  with,  322 
Reversibility  of  cells,  236 
Revolving  armature,  alternators  with, 

641 

Revolving  field,  alternators  with,  642 
Rheostat,  302,  513,  600 
Right    hand    rule    for    deflection    of 

needle,  345 
for  direction  of  induced  E.  M.  F., 

422 

Ring  transformer,  649 
Ring  wound  armature,  566 
Ring  wound  generator,  569 
Rocker  frame,  568 
Rontgen  rays,  678 
Rotary  converter,  653 
Rotating  coil,  E.  M.  F.  of,  552 
in  magnetic  field,  551 
production  of  current  by,  553 
Rotating  field,  production  of,  664 
Rotation  of  current  by  magnetic  pole, 

351 

Rotation  of  motor,  direction  of,  604 
Rotation  of  pole  by  current,  350 
Rotor,  665 
Rule  for  direction  of  field  about  wire 

carrying  current,  348 
for  direction  of  induced  E.  M.  F., 

421,  422 
for    direction    of    motion    of    wire 

carrying  a  current,  352 
for  deflection  of  needle  by  current, 

345 

for  polarity  of  electro-magnet,  404 
Salt,  electrolysis  of  a,  224 
Saturation,  magnetic,  393 
Schweigger's  multiplier,  365 

graphs,  678 
Screen,  magnetic,  113,  143 


Second,  mean  solar,  9 
Secondary  cell,  237 

elements  of,  238 
Seebeck's  discoveries,  528 
Selenium,  285 

Self-excitation,  methods  of,  563 
Self-induction,  432,  614 

absolute  unit  of,  433 

measure  of,  433 

practical  unit  of,  433,  434 
Semicircular  variation,  183 
Sensitiveness  of  relay,  705 

of  telephone,  705 

Separation  of  induced  charges,  32 
Series,  thermo-electric,  528 
Series  generator,  563,  582 

characteristic  of,  585 
Series  grouping  of  cells,  335,  337 
Series  motor,  602 

speed  of,  603 

Series  motor  for  A.  C.,  659 
Shape  of  electro-magnets,  407 
Shell  transformer,  649 
Shells,  magnetic,  369 
Shifting  of  brushes,  570,  571,  598 
Short  circuit,  306 
Shunt,  ammeter,  465,  466 

defined,  293 

division  of  current  by,  301 

galvanometer,  need  of,  380 

millivoltmeter,  475 

switchboard,  466 

universal,  381 
Shunt  generator,  563,  582,  587 

characteristic,  587 
Shunt  motor,  599 

control  of  speed,  600 
Siberian  oval,  170 
Siemens,  543 
Siemens'  electro-dynamometer,  383 

unit  of  resistance,  543 
Silicon  as  detector,  705 
Simple  cell,  193 

chemical  action  in,  195 

dissociation  theory  applied  to,  279 
Sine  galvanometer,  376 
Sine  law,  147 
Single  phase  alternators,  640,  644 


594 


INDEX. 


Single  phase  current,  rectification  of, 

655 

Slide  wire  bridge,  325 
Slip  rings,  642 
Smashing  point  of  incandescent  lamp, 

511 
Solenoid,  385 

effect  of  core  on  field,  390 

equivalent  to  bar  magnet,  386 

intensity  of  field  on  axis,  387 

variation  of  field  with  current,  389 
Solution,  magnetization  favored  by, 

159 

Solution  tension,  278 
Sounder,  412,  704 
Spark  plug,  438 
Sparking,  572 
Specific  reluctance,  400 
Specific  resistance,  285,  288 
Speed  of  series  motor,  603 

of  shunt  motor,  600 
Spheres,  two  coalescing,  82 

two  united,  81 
Spider,  565 
Split  ring,  556,  567 
Standard  cell,  Clark's,  212 

need  of,  211 

Weston's,  213 
Standard  wave  length,  706 
Star  development  of  drum  winding, 

577 

Star  grouping,  647 
Starting  box,  601 
Static  transformer,  649,  656 
Stator,  665 

Storage  battery,  charging,  245,  246, 
415,  582 

charging  from  A.  C.,  655 

defined,  237 

Edison,  250 

advantages,  253 
charging,  252 
reactions  of,  251 

uses  of,  254 

Storage   battery   plates,    dimensions, 
242 

grouping  of,  243 

preparation  of,  239 


Storms,  magnetic,  180 
Strength  of  magnets,  125,  406 
Sturgeon,  403 
Substances,  magnetic,  121 

subject  to  electrolysis,  221 
Surface  density  of  charge,  41,  65,  66 
Suspended  coil  galvanometer,  378 
Switch,  overload,  414 

underload,  414,  582 
Switchboards,  579,  580 
Switchboard  shunt,  465,  466 
Symmer's  theory  of  electricity,  27 
Synchronous  converter,  653 
Synchronous  motor,  660 

operation  of,  661 
Table  of  dimensional  formulae,  547 

of  magnetic  elements,  175 

wire,  295 
Tangent  galvanometer,  373,  546 

measurement  of  current  by,  374 

principle  of,  375 
Tangent  law,  146 
Tantalum  lamp,  507 
Telegraph,  electric,  411 

Morse,  412 

Telegraph  system,  American,  413 
Telegraphy,  wireless,  698 
Telephone,  440 

in  wireless  telegraphy,  705 

operation  of,  442 

sensitiveness  of,  705 
Temperature,  absolute,  256 
Temperature  of  arc,  485 

variation  of  resistance  with,  289 
Temperature  coefficient  of  resistance, 

289 
Tension,  solution,  278 

vapor,  277 
Terminology  of  electrolysis,  Faraday's, 

220 

Terrella,  Gilbert's,  110 
Theory,  dissociation,  applied  to  sim- 
ple cell,  279 

Theory,    dissociation,    of    Arrhenius, 
268 

Grotthus',  274 

of  attracted  disc  electrometer,  102 

of  earth's  magnetism,  181 


INDEX. 


595 


Theory,  etc. — Continued. 

of  electrolytic  dissociation,  extreme 
scope  of,  281 

of  magnetism,  Ewing's,  153,  395 

of  quadrant  electrometer,  104 
Theories  of  electricity,  27 
Thermometer,  platinum,  290 
Thermopile,  532 
Thermo-couple,  528 
Thermo-electric  E.  M.  F.,  528 
Thermo-electric  inversion,  529 
Thomson,  J.  J.,  681,  682,  683 
Thomson,  Sir  William,  see  Kelvin 
Thomson  effect,  531 
Thomson   inclined   coil   instruments, 

471 

Thomson's   proof  of  oscillatory  dis- 
charge, 687 

Three  wire  system,  581 
Thunder  storm,  explanation  proposed, 

82 

Time,  unit  of,  9 
Toepler's  influence  machine,  49 
Torsion,  law  of,  52,  127 
Torsion  balance,  Coulomb's,  52,  100, 

127,  132 

Tractive  power  of  magnet,  406 
Transformation  of  D.  C.  and  A.  C., 

648 
Transformer,  431,  649 

auto,  652 

core,  649 

Faraday's  ring,  431 

operation  of,  650 

ring,  649 

shell,  649 

static,  649,  656 

step  down,  431 

step  up,  431 
Transformers,  connection  of,  651 

use  with  A.  C.  instruments,  472 
Transmission  of  power,  electrical,  501, 

502 
Transmitter,  Blake,  441 

wireless,  700 

Tri-phase  alternator,  645,  646,  647 
Tri-phase  delta  grouping,  646 

Y  connection,  647 


Troubles  of  lead  batteries,  247 
Tube,  Crookes',  670,  671,  672,  675, 

676,  677,  678,  682 
focusing,  678 
Geissler,  670 
Tubes  of  force,  62 
Tungsten  lamp,  507,  512 
Tuning  of  coupled  circuits,  702 
of  receiving  circuits,  706 
of  resonator,  697 
Turning  moment  of  magnet,  149 
Ultra-violet  light,  680 
Underload  switch,  415,  582 
Unit  of  capacity,  practical,  95 
of  current,  536 

absolute,  355,  536,  546 
practical,  228,  307,  448,  546 
of  E.  M.  F.,  537 

absolute,  426,  537,  546 
practical,  77,  427 
of  electric  power,  absolute,  496 
commercial,  496 
practical,  496 

of  electric  work,  commercial,  496 
of  force,  11 
of  heat,  11,  478 
of  length,  7 
of  mass,  8 
of  quantity,  536 
practical,  228 

of  resistance,  absolute,  427,  546 
practical,  284,  546 
Siemens',  543 
of  self-induction,  absolute,  433 

practical,  433,  434 
of  time,  9 
of  work,  11 
Units,  absolute,  11 
electro-magnetic,  535 

primary,  538 
electro-static,  535 
fundamental,  3 

Unit  charge,  lines  of  force  from,  63 
Unit  electric  field,  58,  61 
Unit  jars,  99 
Unit  magnet  pole,  133 
Unit  quantity  of  electricity,  56 
Universal  shunt,  381 


596 


INDEX. 


Use  of  electro-magnets,  408 

of  storage  batteries,  254 
Useful  volts,  305 
Vacua,  discharge  through  high,  670 

through  moderate,  668 
Value  of  alternating  current,  612,  613 
Value  of  electro-magnet,  405 
Van't  Hoff's  generalization,  266 

exceptions  to,  267 
Vapor  tension,  277 
Variation,  magnetic,  169 
Variation  of  magnetic  elements,  176 

of  osmotic  pressure,  263,  264,  265, 
266 

semicircular,  183 
Vector  diagram,  610 
Velocity,  resistance  expressed  as  a,  541 

of  corpuscles,  683 

of  propagation  of  electric  wave,  693, 

694 

Versorium,  16 

Vibration,  loss  of  magnetization  facili- 
tated by,  157 

magnetization  facilitated  by,  156 
Virtual  amperes  and  volts,  612 
Volt,  77,  78,  427,  537,  545,  546 

denned,  307,  427,  545,  546 

international,  212 
Volts,  lost  and  useful,  305 

virtual,  612 

Volta,  35,  186, 187, 188, 190, 191,  218 
Volta's  circlet  of  cups,  191 

contact  series,  187 

contact  theory,  188 

investigations,  186 
Voltaic  cell,  requirements  of,  200 
Voltaic  pile,  190 
Voltameter,  227 

Voltmeter,  455,  458,  459,  460,  468, 
470,  471,  472 

connection  of,  458,  459 

measurement  of  E.  M.  F.  by,  460, 
461 

reading  across  counter  E.  M.  F.,  595 

resistance  of,  458,  459,  460,  461,  468 

Weston  D.  C.,  468 

Weston  D.  C.  A.  C.,  470 
Voltmeters  classified,  462 


Water,  decomposition  of,  218 

electrolysis  of,  219 
Watt,  493 
Watt,  the,  496 
Wattmeter,  indicating,  499 

integrating,  500 

recording,  499,  500 
Waves,  electric,  690,  694 

length  of,  696,  702 

velocity  of  propagation,  693 
Wave  length,  standard,  706 
Wave  meter,  706 
Wave  winding,  575 
Weber,  153 

Weber's  electro-dynamometer,  382 
Weights,  lifting  by  electro-magnets, 

409 

Welding,  electric,  484 
Weston  A.  C.  ammeter,  467 

D.  C.  voltmeter,  468 

D.  C.  A.  C.  voltmeter,  470 

standard  cell,  213 

Wheatstone  bridge,   arrangement  of 
resistances,  315 

evolution  in  form,  316 

measurement  of  resistances  by,  317, 
318,  319,  320,  321 

principle  of,  313,  314 
Whirl,  electric,  44 
Wind,  electric,  42,  44,  48,  49,  50 
Wire  carrying  a  current  not  a  magnet, 

349 

Wire,  circular  measure  of,  296 
Wires,  electric  heating  of,  480,  481 
Wire  gauges,  295 
Wire  tables,  295 
Wireless  telegraphy,  698 

condition  affecting,  707 

distance  attained  by,  707 
Work  done  by  electric  current,  47€ 
Work  in  moving  coil  across  field,  358 

in  moving  conductor  across  field,  357 
Work,  unit  of,  11 

electric,  commercial  unit  of,  496 
X  rays,  678,  679,  680,  684 
Y  connection,  647 
Yoke,  561 
Zincite  as  detector,  705 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


MAY     6   1948 

'53 

v  J 


LD  21-100m-9,'47(A5702sl6)476 


YC    ! 1 270 


